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Ms. Li has 3 classes of students, with 25 students in each class. She wants to give each student 4 pencils and 2 erasers as a welcome gift. If pencils come in packs of 12 and erasers come in packs of 6, how many packs of pencils and erasers should Ms. Li buy in total?

To find the total number of packs of pencils and erasers Ms. Li should buy, let's break down the problem step by step. 1. First, calculate the total number of students in all classes: 3 classes * 25 students/class = <<3*25=75>>75 students. 2. Calculate the total number of pencils needed: 75 students * 4 pencils/student = <<75*4=300>>300 pencils. 3. Since pencils come in packs of 12, divide the total number of pencils by 12 to find the number of packs needed: 300 pencils / 12 pencils/pack = <<300/12=25>>25 packs of pencils. 4. Next, calculate the total number of erasers needed: 75 students * 2 erasers/student = <<75*2=150>>150 erasers. 5. Since erasers come in packs of 6, divide the total number of erasers by 6 to find the number of packs needed: 150 erasers / 6 erasers/pack = <<150/6=25>>25 packs of erasers. 6. Finally, add the number of packs of pencils and erasers to find the total number of packs Ms. Li should buy: 25 packs + 25 packs = <<25+25=50>>50 packs. Therefore, Ms. Li should buy 50 packs in total. #### 50

Question: Luana is making traditional Brazilian jewelry for a local festival. She has 15 beads on each necklace and wants to make 8 necklaces. If she already has 96 beads, how many more beads does she need to buy?

To find out how many more beads Luana needs, let's first calculate the total number of beads required for 8 necklaces: 1. Each necklace requires 15 beads. 2. For 8 necklaces, the total number of beads needed is: 8 necklaces * 15 beads/necklace = <<8*15=120>>120 beads 3. Luana already has 96 beads. 4. To find out how many more beads she needs, we subtract the beads she has from the total beads needed: 120 beads (needed) - 96 beads (already has) = <<120-96=24>>24 beads Therefore, Luana needs to buy 24 more beads to make 8 necklaces. #### 24

Question: Anastasia invests 5000 rubles in a savings account with an annual interest rate of 5%. If the interest is compounded annually, how much will Anastasia have in her account after 3 years?

Let's solve this step-by-step: 1. First, understand the formula for compound interest: A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), and n is the number of years. 2. Given values are: P = 5000 rubles, r = 5% or 0.05 (as a decimal), and n = 3 years. 3. Plug the given values into the compound interest formula: A = 5000(1 + 0.05)^3 4. Calculate inside the parentheses first: 1 + 0.05 = <<1 + 0.05 = 1.05>> 5. Now, raise 1.05 to the power of 3: 1.05^3 = <<1.05^3 = 1.157625>> 6. Multiply the principal amount by this value to find the amount after 3 years: 5000 * 1.157625 = <<5000 * 1.157625 = 5788.125>> Therefore, Anastasia will have 5788.125 rubles in her account after 3 years. #### 5788.125

Ramesh is preparing for the annual Diwali festival and wants to make 300 samosas for his guests. His samosa recipe requires a specific ratio of ingredients to ensure the perfect blend of spices and texture. For every 10 samosas, he needs 2 cups of flour, 1 cup of potatoes, and 1/2 cup of peas. If he already has 20 cups of flour, how many cups of potatoes and peas should he buy to make 300 samosas, considering he wants to have 10% more potatoes and peas than the recipe calls for, and then determine the total cost if potatoes cost $1.20 per cup and peas cost $0.80 per cup?

Let's solve this step by step: 1. First, determine the total amount of each ingredient needed for 300 samosas without the extra 10%: a) Flour: 300 samosas / 10 samosas = <<300/10=30>>30 sets b) Since Ramesh already has 20 cups of flour, and he needs 2 cups per set, he has enough flour for the recipe. c) Potatoes: 30 sets * 1 cup/set = <<30*1=30>>30 cups d) Peas: 30 sets * 0.5 cups/set = <<30*0.5=15>>15 cups 2. Calculate the additional 10% of potatoes and peas Ramesh wants to buy: a) Potatoes: 10% of 30 cups = <<30*0.1=3>>3 cups b) Peas: 10% of 15 cups = <<15*0.1=1.5>>1.5 cups 3. Find the total amount of potatoes and peas Ramesh should buy, including the extra 10%: a) Potatoes: 30 cups + 3 cups = <<30+3=33>>33 cups b) Peas: 15 cups + 1.5 cups = <<15+1.5=16.5>>16.5 cups 4. Calculate the total cost of potatoes and peas: a) Potatoes: 33 cups * $1.20/cup = $<<33*1.2=39.60>>39.60 b) Peas: 16.5 cups * $0.80/cup = $<<16.5*0.8=13.20>>13.20 c) Total cost = $39.60 + $13.20 = $<<39.6+13.2=52.80>>52.80 Therefore, Ramesh should buy 33 cups of potatoes and 16.5 cups of peas, and the total cost will be $52.80. #### 52.80

Ariel is building a scale model of the Western Wall in Jerusalem for her history class. The actual wall is 488 meters long, and Ariel wants her model to be 1/200th of the real size. If she has a piece of cardboard that is 3 meters long, how many models of the Western Wall can she make from it?

To find out how many models Ariel can make, we first need to calculate the length of one model. Since the model is 1/200th of the real size, we multiply the actual length by 1/200. Model length = 488 meters * (1/200) = <<488 * 1/200 = 2.44>> meters Now, we know the length of one model is 2.44 meters. To find out how many models Ariel can make from her 3-meter cardboard, we divide the total length of the cardboard by the length of one model. Number of models = Total cardboard length / Model length = 3 meters / 2.44 meters = <<3 / 2.44 = 1.23>> Since Ariel cannot make a fraction of a model, we take the floor of 1.23, which is 1. This means she can make 1 full model from her cardboard. #### 1

Tomás has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. Tomás' parents have agreed to give him an allowance of $5 per week for doing chores. How many weeks will Tomás have to do chores to have enough money to buy the bike?

Let's break this down step by step: 1. Tomás has $120 and needs $180 for the bike. 2. To find out how much more money Tomás needs, we subtract the amount he has from the price of the bike: $180 - $120 = <<180-120=60>>$60 3. Since Tomás gets $5 per week for doing chores, we need to find out how many weeks it will take him to save $60: $60 ÷ $5 = <<60/5=12>>12 weeks Therefore, Tomás will have to do chores for 12 weeks to have enough money to buy the bike. #### 12

Takashi is the student council treasurer at Tokyo High School. The council is planning a school festival and has allocated ¥50,000 for decorations. However, due to budget cuts, they need to reduce the budget by 15%. Then, they receive a 10% discount coupon for the remaining amount from a local decoration supplier. If they decide to spend 70% of the final budget on balloons and the rest on streamers, how much will they spend on streamers?

Let's solve this step-by-step: 1. First, we need to calculate the reduced budget after the 15% cut: Original budget = ¥50,000 Reduction = 15% of ¥50,000 = <<15 * 50000 / 100 = 7500>>¥7,500 New budget = ¥50,000 - ¥7,500 = <<50000 - 7500 = 42500>>¥42,500 2. Then, we apply the 10% discount to the new budget: Discount = 10% of ¥42,500 = <<10 * 42500 / 100 = 4250>>¥4,250 Final budget = ¥42,500 - ¥4,250 = <<42500 - 4250 = 38250>>¥38,250 3. Now, we need to calculate the amount spent on balloons (70% of the final budget): Amount for balloons = 70% of ¥38,250 = <<70 * 38250 / 100 = 26775>>¥26,775 4. The amount spent on streamers is the remaining 30% of the final budget: Amount for streamers = 30% of ¥38,250 = <<30 * 38250 / 100 = 11475>>¥11,475 Therefore, the student council will spend ¥11,475 on streamers. #### 11475

Akira is planning a trip from Tokyo to Osaka, which is approximately 560 kilometers away. If her train travels at an average speed of 80 kilometers per hour for the first 200 kilometers, then increases its speed to 120 kilometers per hour for the next 160 kilometers, and finally slows down to 90 kilometers per hour for the remaining distance, how many hours will the total trip take?

Let's break this down step by step: 1. First, we calculate the time taken for the first 200 kilometers at 80 kilometers per hour: Time = Distance / Speed = 200 km / 80 km/h = <<200/80=2.5>>2.5 hours 2. Next, we calculate the time taken for the next 160 kilometers at 120 kilometers per hour: Time = Distance / Speed = 160 km / 120 km/h = <<160/120=1.3333>>1.3333 hours 3. Then, we calculate the remaining distance after the first two segments: Remaining distance = Total distance - Distance covered = 560 km - 200 km - 160 km = <<560-200-160=200>>200 km 4. Now, we calculate the time taken for the remaining 200 kilometers at 90 kilometers per hour: Time = Distance / Speed = 200 km / 90 km/h = <<200/90=2.2222>>2.2222 hours 5. Finally, we add up the times for all three segments to find the total trip time: Total time = 2.5 hours + 1.3333 hours + 2.2222 hours = <<2.5+1.3333+2.2222=6.0555>>6.0555 hours Therefore, the total trip will take approximately 6.0555 hours. #### 6.0555

Mei-Ling's family is planning a traditional Chinese New Year dinner, and they want to package 480 dumplings into boxes that hold either 8 or 12 dumplings each. If they use all the boxes they have, which hold a total of 48 rows of dumplings, and each row can contain either 8 or 12 dumplings, how many boxes of each size should they use to package all the dumplings?

Let's solve this step-by-step: 1. First, let's define variables: Let x be the number of boxes holding 8 dumplings, and y be the number of boxes holding 12 dumplings. 2. The total number of dumplings packaged should equal 480, so we can write the equation based on the number of dumplings per box: 8x + 12y = 480. 3. We also know the total number of rows is 48. Since each box contributes one row, the total number of boxes (x + y) should equal 48: x + y = 48. 4. Solve the system of equations. First, isolate x in the second equation: x = 48 - y. 5. Substitute x in the first equation: 8(48 - y) + 12y = 480. 6. Simplify and solve for y: 384 - 8y + 12y = 480. 7. Combine like terms: 4y = 480 - 384 = <<480 - 384 = 96>>96. 8. Solve for y: y = 96 / 4 = <<96 / 4 = 24>>24. 9. Substitute y back to find x: x = 48 - 24 = <<48 - 24 = 24>>24. 10. Mei-Ling's family should use 24 boxes of 8 dumplings and 24 boxes of 12 dumplings to package all the dumplings. Therefore, the solution is found, but to follow the format exactly, we need a numeric answer. Since the question asks for the number of boxes of each size but the format requires a single number, it seems there might be a misunderstanding in the problem's requirement for the answer format. However, following the instructions to provide a numeric answer and given the solution involves two values (24 boxes of 8 and 24 boxes of 12), we'll present the answer as a combined total of boxes used which is 24 + 24 = <<24 + 24 = 48>>48 boxes in total. #### 48

In the Korean Basketball League, Team Seoul has a 60% chance of winning against Team Busan in a single game. If they play a best-of-five series, what is the probability that Team Seoul will win the series in exactly four games?

To solve this, let's break it down step by step: 1. **Understanding the Problem**: We are looking for the probability that Team Seoul wins the series in exactly four games. This means they must win three games out of the first four, and then win the fifth game is not considered in this scenario as we are calculating for exactly four games. 2. **Identifying Possible Scenarios**: For Team Seoul to win in exactly four games, they must win three out of the first four games. The possible scenarios for winning three out of the first four games are: - Winning the first three games and losing the fourth. - Winning the first, second, and fourth games, and losing the third. - Winning the first, third, and fourth games, and losing the second. - Winning the second, third, and fourth games, and losing the first. 3. **Calculating the Probability of Each Scenario**: The probability of Team Seoul winning a game is 60% (or 0.6), and the probability of losing is 40% (or 0.4). - The probability of winning the first three games and losing the fourth is: \(0.6^3 \times 0.4 = <<0.6^3 * 0.4 = 0.0864>>\). - Similarly, the probability for each of the other scenarios is also \(0.6^3 \times 0.4\), since the order of wins and losses does not affect the overall probability of the sequence occurring. 4. **Calculating the Total Probability**: Since these scenarios are mutually exclusive (they cannot happen at the same time), we add the probabilities together. - The total probability is \(4 \times 0.0864 = <<4 * 0.0864 = 0.3456>>\). Therefore, the probability that Team Seoul will win the series in exactly four games is \(0.3456\), or \(34.56\%\). #### 0.3456

Maya is making shakshuka for her family dinner and wants to adjust the recipe to serve 8 people instead of 4. If the original recipe calls for 2 cups of chopped tomatoes, how many cups will Maya need for her scaled-up recipe?

Let's solve this step by step: 1. First, we need to find the scaling factor to adjust the recipe from 4 people to 8 people. This can be done by dividing the number of people we want to serve by the number of people the original recipe serves: 8 / 4 = <<8/4=2>>2. 2. Since we are scaling up the recipe, we will multiply the original amount of chopped tomatoes by the scaling factor to find the new amount needed: 2 cups * 2 = <<2*2=4>>4 cups. Therefore, Maya will need 4 cups of chopped tomatoes for her scaled-up recipe. #### 4

Hans is saving money for a new bike that costs €240. He has already saved €120 and plans to mow lawns to earn more. If he charges €8 per lawn and wants to buy the bike in 5 weeks, how many lawns does he need to mow each week to have enough money?

Let's solve this step by step: 1. First, we need to find out how much more money Hans needs to save to buy the bike: Total cost of the bike = \u20ac240 Amount already saved = \u20ac120 Amount still needed = Total cost - Amount already saved = \u20ac240 - \u20ac120 = <<240 - 120 = 120>>\u20ac120 2. Next, we need to figure out how many lawns Hans needs to mow in total to earn the remaining amount: Earnings per lawn = \u20ac8 Total earnings needed = \u20ac120 Total lawns needed = Total earnings needed / Earnings per lawn = \u20ac120 / \u20ac8 = <<120 / 8 = 15>>15 lawns 3. Since Hans wants to buy the bike in 5 weeks, we need to calculate how many lawns he needs to mow each week: Total lawns needed = 15 Number of weeks = 5 Lawns per week = Total lawns needed / Number of weeks = 15 / 5 = <<15 / 5 = 3>>3 lawns per week Therefore, Hans needs to mow 3 lawns per week to save enough money for the bike in 5 weeks. #### 3

Mme Dupont, a French teacher, has been saving money for a school trip to Paris. She initially invested €1,500 in a savings account with an annual interest rate of 4%. If the interest is compounded annually, how much will she have after 5 years?

To find out how much Mme Dupont will have after 5 years, we'll calculate the compound interest step by step. 1. First, we need to understand the formula for compound interest, which is A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), and n is the number of years. 2. Given that the initial investment P is €1,500, the annual interest rate r is 4% or 0.04 in decimal form, and the interest is compounded annually for 5 years, we can plug these values into the formula. 3. Convert the annual interest rate to decimal form: r = 4% = 0.04. 4. Now, we apply the compound interest formula: A = 1500(1 + 0.04)^5. 5. Calculate the amount inside the parentheses first: (1 + 0.04) = <<1 + 0.04 = 1.04>>. 6. Raise 1.04 to the power of 5 to account for the 5 years: 1.04^5 = <<1.04^5 = 1.216647398950907>>. 7. Multiply the principal amount by the result to find the total amount after 5 years: 1500 * 1.216647398950907 = <<1500 * 1.216647398950907 = 1824.971098713361>>. Therefore, Mme Dupont will have approximately €1,825 after 5 years. #### 1825

Mrs. Thompson is planning a bake sale at Springdale Middle School in Toronto. She orders 250 cupcakes and wants to package 25% of them in boxes of 5 for a special promotion. How many boxes can she fill with the cupcakes set aside for the promotion?

Let's solve this step by step: 1. First, we need to find out how many cupcakes Mrs. Thompson wants to set aside for the promotion. This is 25% of 250 cupcakes: 25% of 250 = <<25/100 * 250 = 62.5>> cupcakes Since we can't have a fraction of a cupcake, we round down to the nearest whole number that can be evenly divided by 5 (to fill the boxes): 62.5 → 60 cupcakes 2. Now, we divide the number of cupcakes for the promotion by the number of cupcakes per box to find out how many boxes can be filled: 60 cupcakes / 5 cupcakes per box = <<60 / 5 = 12>> boxes Therefore, Mrs. Thompson can fill 12 boxes with the cupcakes set aside for the promotion. #### 12

Maya, a wildlife biologist in the Canadian Rockies, is studying the habitat of a local bird species. The area of the habitat can be modeled by the polynomial 2x^2 + 5x - 3, where x is the number of kilometers from the nearest lake. If a severe storm reduces the habitat by a factor of x - 1, what is the new area of the habitat when x = 3?

To find the new area of the habitat after the storm, we first need to understand the initial area and how it's affected by the storm. The initial area is given by the polynomial 2x^2 + 5x - 3. Since the storm reduces the habitat by a factor of x - 1, we'll need to multiply the initial area by this factor to find the new area. Step 1: Identify the initial area polynomial and the reduction factor. Initial area = 2x^2 + 5x - 3 Reduction factor = x - 1 Step 2: Substitute x = 3 into the reduction factor to find the specific reduction at this distance. Reduction factor at x = 3 = 3 - 1 = <<3-1=2>> Step 3: Substitute x = 3 into the initial area polynomial to find the initial area at this distance. Initial area at x = 3 = 2(3)^2 + 5(3) - 3 = 2(9) + 15 - 3 = 18 + 15 - 3 = <<18+15-3=30>> Step 4: Multiply the initial area by the reduction factor to find the new area. New area = Initial area * Reduction factor = 30 * 2 = <<30*2=60>> Therefore, the new area of the habitat when x = 3 is 60 square kilometers. #### 60

Tommy scored 85, 90, and 78 on his first three math tests. If the next test is worth the same as the previous tests, and he wants to have an average score of at least 88, what is the minimum score he needs to achieve on his fourth test?

Let's solve this step-by-step: 1. First, we need to find the total score Tommy has achieved so far: Total score so far = 85 + 90 + 78 = <<85+90+78=253>>253 2. Since there are four tests in total and he wants an average score of at least 88, we need to find the total score he needs to achieve: Total score needed = Average score * Number of tests = 88 * 4 = <<88*4=352>>352 3. To find the minimum score he needs on the fourth test, we subtract the total score he has so far from the total score he needs: Minimum score needed on the fourth test = Total score needed - Total score so far = 352 - 253 = <<352-253=99>>99 Therefore, Tommy needs to achieve a minimum score of 99 on his fourth test. #### 99

Rahul is planning a bird-watching trip to the Western Ghats in India. He wants to visit two bird sanctuaries, A and B, which are 150 km apart. The cost of visiting sanctuary A is ₹500 per person, and the cost of visiting sanctuary B is ₹700 per person. The transportation cost between the two sanctuaries is ₹200 per person. Rahul has a budget of ₹2,500 for the entire trip. If he wants to maximize the number of people he can take on the trip, how many people can he take to both sanctuaries A and B?

To maximize the number of people Rahul can take on the trip, we need to minimize the cost per person. Let's calculate the total cost for visiting both sanctuaries A and B: 1. Cost of visiting sanctuary A: \u20b9500 per person 2. Cost of visiting sanctuary B: \u20b9700 per person 3. Transportation cost between the two sanctuaries: \u20b9200 per person Total cost per person = Cost of A + Cost of B + Transportation cost Total cost per person = \u20b9500 + \u20b9700 + \u20b9200 Total cost per person = \u20b9<<500 + 700 + 200 = 1400>>1400 Rahul has a budget of \u20b92,500 for the entire trip. To find the maximum number of people he can take, we divide the total budget by the total cost per person: Maximum number of people = Total budget / Total cost per person Maximum number of people = \u20b92,500 / \u20b91,400 Maximum number of people = <<2500 / 1400 = 1.7857>> Since we can't take a fraction of a person, we round down to the nearest whole number: Maximum number of people = <<floor(1.7857) = 1>> Therefore, Rahul can take 1 person to both sanctuaries A and B to maximize the number of people within his budget. #### 1

The Shanghai Sharks basketball team has played 15 games with a win-loss record of 10-5. In those games, their star player, Li Ming, has scored an average of 25 points per game. If Li Ming's scoring average increases by 15% for the next 5 games, and the team wins 4 out of those 5 games, what will be the team's new win-loss record and Li Ming's new total points scored?

Let's break down the problem step by step: 1. First, let's find Li Ming's total points scored in the first 15 games: Li Ming's average points per game = 25 Total games = 15 Total points = average points per game * total games = <<25 * 15 = 375>>375 points 2. Now, let's calculate Li Ming's new scoring average for the next 5 games, considering the 15% increase: New average = old average + (15% of old average) New average = 25 + (15/100 * 25) = 25 + <<15/100 * 25 = 3.75>>3.75 = <<25 + 3.75 = 28.75>>28.75 points per game 3. Calculate Li Ming's total points scored in the next 5 games: New total points = new average points per game * total games = <<28.75 * 5 = 143.75>>143.75 points 4. Calculate Li Ming's new total points scored for all 20 games: New total points = total points in first 15 games + total points in next 5 games = 375 + 143.75 = <<375 + 143.75 = 518.75>>518.75 points 5. Determine the team's new win-loss record after winning 4 out of the next 5 games: Previous record: 10-5 Additional wins: 4 Additional losses: 1 New record: (10 + 4) - (5 + 1) = 14 - 6 So, the new win-loss record is 14-6. 6. Since the question asks for the new win-loss record and Li Ming's new total points scored, we'll provide both answers. 7. However, as per the format, we need to provide a single numeric answer. The question seems to be asking for two different values, which doesn't fit the required format. To follow the format, we'll provide Li Ming's new total points scored as the final answer, assuming that's the primary value of interest. 8. Therefore, Li Ming's new total points scored is 518.75. #### 518.75

Ms. Tremblay is planning a school trip to the Canadian Museum of History for her grade 11 class. The bus rental company offers two types of buses: a standard bus that can seat 45 students and a larger bus that can seat 60 students. The ratio of boys to girls in the class is 3:5, and there are a total of 120 students in the class. If the standard bus costs $800 to rent and the larger bus costs $1,200 to rent, what is the most cost-effective way for Ms. Tremblay to transport her students to the museum, and how much will it cost in total?

To solve this problem, we need to determine the number of boys and girls in the class and then decide which buses to rent to accommodate them in the most cost-effective way. 1. Calculate the number of boys and girls in the class: Given the ratio of boys to girls is 3:5, we can find the total parts as 3 + 5 = <<3+5=8>>8 parts. Since there are 120 students in total, each part represents 120 / 8 = <<120/8=15>>15 students. Therefore, the number of boys is 3 parts * 15 students/part = <<3*15=45>>45 boys. And the number of girls is 5 parts * 15 students/part = <<5*15=75>>75 girls. 2. Determine the number of buses needed: Since there are 45 boys and 75 girls, we need to accommodate 45 + 75 = <<45+75=120>>120 students in total. 3. Calculate the number of standard buses needed: If we use only standard buses, we would need 120 students / 45 students/bus = <<120/45=2.67>>2.67 buses, which means we actually need 3 standard buses because we cannot rent a fraction of a bus. 4. Calculate the cost of using standard buses: 3 standard buses * $800/bus = $<<3*800=2400>>2,400. 5. Calculate the number of larger buses needed: If we use only larger buses, we would need 120 students / 60 students/bus = <<120/60=2>>2 buses. 6. Calculate the cost of using larger buses: 2 larger buses * $1,200/bus = $<<2*1200=2400>>2,400. 7. Compare the costs and decide on the most cost-effective option: Both options cost the same, $2,400. However, using larger buses might be more convenient as it requires fewer buses. Therefore, Ms. Tremblay should rent 2 larger buses to transport her students to the museum in the most cost-effective way. 8. Calculate the total cost: The total cost will be $2,400. #### 2400

Amit and his friends are planning a camping trip in the Negev Desert. They want to share some snacks equally among themselves. Amit has 18 bags of Bamba, his friend Rachel has 25 bags of pretzels, and his other friend, David, has 32 bags of popcorn. If they want to put an equal number of bags in each of their 5 cars, how many bags of snacks will each car have?

To find out how many bags of snacks each car will have, we need to follow these steps: 1. First, we calculate the total number of bags of snacks: Total bags = Amit's bags + Rachel's bags + David's bags Total bags = 18 + 25 + 32 <<18 + 25 + 32 = 75>> bags 2. Next, we need to divide the total number of bags by the number of cars to find out how many bags each car will have: Bags per car = Total bags / Number of cars Bags per car = 75 / 5 <<75 / 5 = 15>> bags Therefore, each car will have 15 bags of snacks. #### 15

Élise wants to make a set of handmade jewelry for her friends. She needs 5 beads for a necklace and 3 beads for a bracelet. If she has 48 beads available and wants to make as many sets as possible, how many necklaces and bracelets can she make in total?

Let's solve this step by step: 1. Define variables: Let x be the number of necklaces and y be the number of bracelets Élise can make. 2. Each necklace requires 5 beads, and each bracelet requires 3 beads. Élise has 48 beads available, so we can set up the equation: 5x + 3y ≤ 48 3. Since Élise wants to make as many sets as possible, we want to maximize the total number of necklaces and bracelets. This can be achieved by first maximizing the number of necklaces (as they require more beads) and then using the remaining beads for bracelets. 4. First, find the maximum number of necklaces that can be made with 48 beads: 48 ÷ 5 = <<48 / 5 = 9.6>> (round down to 9 since we can't make a fraction of a necklace) So, Élise can make 9 necklaces, using 9 * 5 = <<9 * 5 = 45>> beads. The remaining beads are 48 - 45 = <<48 - 45 = 3>> beads. With 3 beads, she can make 3 ÷ 3 = <<3 / 3 = 1>> bracelet. Therefore, the total number of necklaces and bracelets Élise can make is 9 + 1 = <<9 + 1 = 10>>. #### 10

Ayşe is the president of the student council at her high school in Istanbul. The council is planning to paint a mural on a rectangular wall in the cafeteria that measures 12 meters by 4 meters. They want to add a triangular section above the rectangle that has a height of 2 meters and a base equal to the width of the rectangle. If a can of paint covers 6 square meters, how many cans will they need to buy to cover the entire area of the mural?

To find the total area of the mural, we need to calculate the area of the rectangle and the area of the triangle separately, then add them together. 1. Calculate the area of the rectangle: Area of rectangle = length * width = 12 * 4 = <<12*4=48>>48 square meters 2. Calculate the area of the triangle: Area of triangle = (base * height) / 2 = (4 * 2) / 2 = <<4*2/2=4>>4 square meters 3. Calculate the total area of the mural: Total area = area of rectangle + area of triangle = 48 + 4 = <<48+4=52>>52 square meters 4. Since a can of paint covers 6 square meters, we need to divide the total area by 6 to find the number of cans needed: Number of cans = total area / 6 = 52 / 6 = <<52/6=8.67>>8.67 cans Since we can't buy a fraction of a can, we'll round up to the nearest whole number. 5. Round up to the nearest whole number: Number of cans = 9 Therefore, the student council needs to buy 9 cans of paint to cover the entire area of the mural. #### 9

Amaka is saving money to buy a new school bag that costs ₦5,000. She already has ₦2,000 and plans to save an additional ₦200 each week from her allowance. How many weeks will it take Amaka to have enough money to buy the school bag?

Let's solve this step by step: 1. First, we need to find out how much more money Amaka needs to save to buy the school bag: Total cost of the bag = \u20a65,000 Money Amaka already has = \u20a62,000 Money needed = Total cost - Money Amaka already has = \u20a65,000 - \u20a62,000 = \u20a63,000 <<5000 - 2000 = 3000>> 2. Amaka saves \u20a6200 each week. To find out how many weeks it will take her to save the needed amount, we divide the money needed by the weekly savings: Number of weeks = Money needed / Weekly savings = \u20a63,000 / \u20a6200 = <<3000 / 200 = 15>> Therefore, it will take Amaka 15 weeks to have enough money to buy the school bag. #### 15

Ms. Rachel, a teacher at Tel Aviv High School, is analyzing the scores of her 25 students in a recent math test. The average score is 78. If the top 5 students scored an average of 95, what is the average score of the remaining 20 students?

To find the average score of the remaining 20 students, let's first calculate the total score of all 25 students. Since the average score is 78, we can multiply this by the number of students to find the total score: Total score = Average score * Number of students Total score = 78 * 25 <<78*25=1950>> Total score = 1950 Next, let's calculate the total score of the top 5 students. Their average score is 95, so we multiply this by the number of top students: Total score of top 5 = Average score of top 5 * Number of top students Total score of top 5 = 95 * 5 <<95*5=475>> Total score of top 5 = 475 Now, we subtract the total score of the top 5 students from the total score of all 25 students to find the total score of the remaining 20 students: Total score of remaining 20 = Total score of all 25 - Total score of top 5 Total score of remaining 20 = 1950 - 475 <<1950-475=1475>> Total score of remaining 20 = 1475 Finally, we divide the total score of the remaining 20 students by the number of remaining students to find their average score: Average score of remaining 20 = Total score of remaining 20 / Number of remaining students Average score of remaining 20 = 1475 / 20 <<1475/20=73.75>> Average score of remaining 20 = 73.75 #### 73.75

Mei is preparing a traditional Chinese dish for a large family gathering. The recipe for her famous dumplings requires a ratio of 3 parts flour to 2 parts water. If she needs 480 grams of flour, how many grams of water should she use?

Let's solve this step-by-step: 1. The recipe requires a ratio of 3 parts flour to 2 parts water. 2. Mei needs 480 grams of flour. 3. To find the amount of water needed, we can set up a proportion based on the ratio of flour to water: 3 parts flour / 2 parts water = 480 grams flour / x grams water 4. We can then solve for x by cross-multiplying: 3x = 2 * 480 3x = <<2 * 480 = 960>> x = 960 / 3 x = <<960 / 3 = 320>> Therefore, Mei should use 320 grams of water. #### 320

Ramesh is planning to make a large batch of chicken tikka masala for a family gathering. The recipe he found serves 8 people and requires 1 1/2 cups of plain yogurt, 2 tablespoons of lemon juice, 2 teaspoons of garam masala, and 1/2 teaspoon of cayenne pepper. If Ramesh wants to serve 24 people, how many cups of plain yogurt will he need in total?

Let's break this down step by step: 1. First, we need to determine the scaling factor to adjust the recipe from 8 people to 24 people. This can be found by dividing the number of people we want to serve by the number of people the original recipe serves: 24 people / 8 people = <<24/8=3>>3 2. This means we need to multiply each ingredient by 3 to scale up the recipe. 3. For the plain yogurt, the original recipe requires 1 1/2 cups. To find the total amount needed, we multiply this by our scaling factor: 1 1/2 cups * 3 = 4 1/2 cups = <<1.5*3=4.5>>4.5 cups Therefore, Ramesh will need 4.5 cups of plain yogurt in total. #### 4.5

Akua is making a batch of her favorite Ghanaian groundnut soup for a family gathering. The recipe calls for 2 cups of groundnuts and serves 8 people. If she wants to make enough soup for 12 people, how many cups of groundnuts should Akua use?

To find out how many cups of groundnuts Akua needs for 12 people, we first need to determine the ratio of groundnuts to people in the original recipe. The recipe calls for 2 cups of groundnuts for 8 people. 1. Calculate the ratio of groundnuts per person: 2 cups / 8 people = <<2/8=0.25>>0.25 cups per person 2. Since Akua wants to make enough soup for 12 people, we can multiply the number of people by the ratio of groundnuts per person: 12 people * 0.25 cups/person = <<12*0.25=3>>3 cups Therefore, Akua should use 3 cups of groundnuts to make enough soup for 12 people. #### 3

The Li family is planning a road trip from Beijing to Shanghai, a distance of 1,200 kilometers. Their car's fuel efficiency is 10 kilometers per liter, and fuel costs 8 yuan per liter. They want to minimize their fuel costs by driving at an optimal speed. At 80 kilometers per hour, their car consumes 8 liters of fuel per hour, but at 60 kilometers per hour, it consumes 6 liters per hour. If they drive for 8 hours a day, how many yuan can they save in fuel costs per day by driving at 60 kilometers per hour instead of 80 kilometers per hour?

To find the fuel cost savings, let's calculate the daily fuel consumption and costs for both speeds. 1. First, let's determine the distance covered in 8 hours at 80 kilometers per hour: Distance = Speed * Time = 80 * 8 = <<80 * 8 = 640>> kilometers 2. Next, calculate the fuel consumption for 640 kilometers at 80 kilometers per hour: Since the car consumes 8 liters of fuel per hour at 80 kilometers per hour, in 8 hours it will consume: Fuel consumption = 8 * 8 = <<8 * 8 = 64>> liters 3. Now, calculate the fuel cost for 64 liters: Fuel cost = Fuel consumption * Fuel price per liter = 64 * 8 = <<64 * 8 = 512>> yuan 4. Then, let's determine the distance covered in 8 hours at 60 kilometers per hour: Distance = Speed * Time = 60 * 8 = <<60 * 8 = 480>> kilometers 5. Calculate the fuel consumption for 480 kilometers at 60 kilometers per hour: Since the car consumes 6 liters of fuel per hour at 60 kilometers per hour, in 8 hours it will consume: Fuel consumption = 6 * 8 = <<6 * 8 = 48>> liters 6. Now, calculate the fuel cost for 48 liters: Fuel cost = Fuel consumption * Fuel price per liter = 48 * 8 = <<48 * 8 = 384>> yuan 7. Finally, calculate the daily fuel cost savings by driving at 60 kilometers per hour instead of 80 kilometers per hour: Daily savings = Fuel cost at 80 km/h - Fuel cost at 60 km/h = 512 - 384 = <<512 - 384 = 128>> yuan Therefore, the Li family can save 128 yuan in fuel costs per day by driving at 60 kilometers per hour instead of 80 kilometers per hour. #### 128

Kaito is saving money to buy a new video game that costs ¥5980. He has a ¥1000 allowance each month and earns an extra ¥500 by walking his neighbor's dog. If he already has ¥1200 and plans to buy the game in 5 months, will he have enough money to afford an additional ¥800 gaming headset?

Let's break this down step by step: 1. Kaito starts with ¥1200. 2. Each month, he gets an allowance of ¥1000 and earns an extra ¥500 from walking the dog, so his total monthly income is: ¥1000 + ¥500 = <<1000 + 500 = 1500>>¥1500 3. Over 5 months, he will earn: ¥1500 * 5 = <<1500 * 5 = 7500>>¥7500 4. Adding this to the money he already has: ¥1200 + ¥7500 = <<1200 + 7500 = 8700>>¥8700 5. The cost of the video game is ¥5980, so after buying it, he will have: ¥8700 - ¥5980 = <<8700 - 5980 = 2720>>¥2720 left 6. The gaming headset costs ¥800, so we need to check if he can afford it with the remaining money: ¥2720 - ¥800 = <<2720 - 800 = 1920>>¥1920 Since this results in a positive amount, he can afford the headset. 7. Therefore, the answer to whether he will have enough money to afford the gaming headset is yes, and the amount left after buying both the game and the headset is ¥1920. #### 1920

Luana is making Brigadeiros, a traditional Brazilian dessert, for her family gathering. The recipe calls for 2 cups of sweetened condensed milk to make 12 Brigadeiros. If Luana wants to make 36 Brigadeiros, how many cups of sweetened condensed milk will she need?

Let's solve this step by step: 1. First, we need to determine the ratio of sweetened condensed milk to the number of Brigadeiros. The recipe calls for 2 cups of sweetened condensed milk to make 12 Brigadeiros. 2. To find the amount of sweetened condensed milk needed for 1 Brigadeiro, we divide the amount for 12 Brigadeiros by 12: 2 cups / 12 Brigadeiros = <<2/12=0.1667>>0.1667 cups per Brigadeiro. 3. Since Luana wants to make 36 Brigadeiros, we multiply the amount needed for 1 Brigadeiro by 36: 0.1667 cups/Brigadeiro * 36 Brigadeiros = <<0.1667*36=6>>6 cups. Therefore, Luana will need 6 cups of sweetened condensed milk to make 36 Brigadeiros. #### 6

During Carnaval in Rio de Janeiro, a street vendor sells 50 traditional Brazilian masks for R$15 each and 75 feather boas for R$8 each. She also offers a special deal of a mask and boa together for R$20. If she sold 30 of the special deals, 15 individual masks, and 45 individual boas, how much money did she make in total?

Let's break this down step by step: 1. Calculate the total amount made from selling the special deals: 30 deals * R$20/deal = <<30*20=600>>R$600 2. Calculate the total amount made from selling the individual masks: 15 masks * R$15/mask = <<15*15=225>>R$225 3. Calculate the total amount made from selling the individual boas: 45 boas * R$8/boa = <<45*8=360>>R$360 4. Add up the amounts made from all the sales to find the total amount of money made: R$600 + R$225 + R$360 = <<600+225+360=1185>>R$1185 Therefore, the street vendor made a total of R$1185. #### 1185

Ngọc and Linh are planning a road trip from Hanoi to Ho Chi Minh City, a distance of 1750 km. If their car travels 250 km in 5 hours, how many hours will it take them to complete the entire trip?

To find the total time it will take Ng\u1ecdc and Linh to complete their trip, we need to first determine the speed of their car. We know that the car travels 250 km in 5 hours. We can calculate the speed as follows: Speed = Distance / Time Speed = 250 km / 5 hours <<250 / 5 = 50>> km/h Now that we know the speed of the car, we can use it to find the total time for the trip. The formula to find time when distance and speed are known is: Time = Distance / Speed Given the total distance is 1750 km and the speed of the car is 50 km/h, we can substitute these values into the formula: Time = 1750 km / 50 km/h <<1750 / 50 = 35>> hours Therefore, it will take Ng\u1ecdc and Linh 35 hours to complete their road trip from Hanoi to Ho Chi Minh City. #### 35

A forest in the French countryside is home to a population of European rabbits that doubles every 3 months. If there are currently 150 rabbits and the forest can sustain a maximum of 1000 rabbits, how many months will it take for the population to reach this limit?

To solve this problem, we'll follow these steps: 1. Understand the growth pattern of the rabbit population. 2. Set up an equation to model this growth. 3. Solve for the time it takes for the population to reach 1000 rabbits. Step 1: Understand the growth pattern. - The rabbit population doubles every 3 months. Step 2: Set up the growth equation. - Let P be the initial population (150 rabbits), and let t be the time in months. - Since the population doubles every 3 months, we can model the population growth using the equation: Population at time t = P * 2^(t/3). Step 3: Solve for t when the population reaches 1000 rabbits. - Set the equation equal to 1000: 150 * 2^(t/3) = 1000. - To solve for t, divide both sides by 150: 2^(t/3) = 1000 / 150 = <<1000 / 150 = 6.67>>. - Since 2^3 = 8, and 2^2 = 4, we know that 2^3 is slightly greater than 6.67, and 2^2 is less than 6.67. Therefore, t/3 must be between 2 and 3. We can solve this by using logarithms or by trial and error with the given options. Step 4: Calculate t using logarithms. - Take the logarithm of both sides: log(2^(t/3)) = log(6.67). - Using logarithm properties, we can simplify this to: (t/3) * log(2) = log(6.67). - Divide both sides by log(2) to isolate t/3: t/3 = log(6.67) / log(2). - Multiply both sides by 3 to solve for t: t = 3 * (log(6.67) / log(2)). Step 5: Calculate the numerical value of t. - Using a calculator: log(6.67) ≈ 0.824, and log(2) ≈ 0.301. - Then, t ≈ 3 * (0.824 / 0.301) ≈ 3 * 2.74 ≈ 8.22 months. Therefore, it will take approximately 8.22 months for the rabbit population to reach 1000 rabbits. #### 8.22

Pierre is planning a trip from Paris to Lyon. The distance between the two cities is 470 kilometers. If Pierre's train travels at an average speed of 120 kilometers per hour, and he has a 15-minute layover, how many hours will the entire trip take?

To find the total time for the trip, we first need to calculate the travel time and then add the layover time. 1. Calculate the travel time: Given distance = 470 kilometers, speed = 120 kilometers per hour Using the formula time = distance / speed Time = 470 km / 120 km/h = <<470 / 120 = 3.9167>> hours 2. Convert the layover time to hours: 15 minutes = 15 / 60 = <<15 / 60 = 0.25>> hours 3. Calculate the total trip time: Total time = travel time + layover time Total time = 3.9167 hours + 0.25 hours = <<3.9167 + 0.25 = 4.1667>> hours Therefore, the entire trip will take approximately 4.17 hours. #### 4.17

The Kuznetsov family is planning a road trip from Moscow to St. Petersburg. The distance between the two cities is 700 kilometers. Their car's fuel efficiency is 10 kilometers per liter, and the current fuel price is 45 rubles per liter. If they want to split the fuel cost equally among the 5 family members, how much will each person have to pay for the round trip?

To find out how much each family member has to pay for the round trip, we need to calculate the total fuel cost for the trip and then divide it by the number of family members. 1. First, we calculate the total distance for the round trip: 700 km * 2 (for round trip) = <<700*2=1400>>1400 km. 2. Then, we determine how much fuel is needed for the trip: Total distance / Fuel efficiency = 1400 km / 10 km/liter = <<1400/10=140>>140 liters. 3. Next, we calculate the total fuel cost: Total fuel needed * Fuel price per liter = 140 liters * 45 rubles/liter = <<140*45=6300>>6300 rubles. 4. Finally, we divide the total fuel cost by the number of family members to find out how much each person has to pay: Total fuel cost / Number of family members = 6300 rubles / 5 = <<6300/5=1260>>1260 rubles. Therefore, each family member will have to pay 1260 rubles for the round trip. #### 1260

During Oktoberfest in Munich, a popular German beer festival, a vendor sells an average of 25 liters of apple cider per hour. If a liter of apple cider costs 5 euros, and the vendor operates for 8 hours a day, how much money does the vendor make in a day?

Let's solve this step-by-step: 1. First, calculate the total amount of apple cider sold in a day: The vendor sells 25 liters of apple cider per hour and operates for 8 hours a day. Total liters sold = 25 liters/hour * 8 hours = <<25*8=200>>200 liters 2. Now, calculate the total money made by the vendor in a day: A liter of apple cider costs 5 euros. Total money made = Total liters sold * Cost per liter = 200 liters * 5 euros/liter = <<200*5=1000>>1000 euros Therefore, the vendor makes 1000 euros in a day. #### 1000

During Oktoberfest, a German bakery is making a special batch of apple strudels for the celebrations. They need to package 3/4 of a bag of sugar, 1/6 of a bag of flour, and 2/3 of a bag of cinnamon into smaller packets for the recipe. If they have 18 bags of sugar, 24 bags of flour, and 12 bags of cinnamon to package, how many packets of each ingredient will they have in total after dividing the ingredients according to the recipe?

To find the total number of packets of each ingredient, we'll calculate the packets for each ingredient separately and then sum them up. 1. First, let's calculate the number of packets of sugar needed: The bakery needs 3/4 of a bag of sugar per packet. With 18 bags of sugar, they can make: 18 bags * (1 bag / (3/4 bag)) = 18 * (4/3) = <<18*4/3=24>>24 packets of sugar. 2. Next, we calculate the number of packets of flour needed: The bakery needs 1/6 of a bag of flour per packet. With 24 bags of flour, they can make: 24 bags * (1 bag / (1/6 bag)) = 24 * 6 = <<24*6=144>>144 packets of flour. 3. Then, we calculate the number of packets of cinnamon needed: The bakery needs 2/3 of a bag of cinnamon per packet. With 12 bags of cinnamon, they can make: 12 bags * (1 bag / (2/3 bag)) = 12 * (3/2) = <<12*3/2=18>>18 packets of cinnamon. 4. Now, we sum up the packets of each ingredient to find the total number of packets: Total packets = packets of sugar + packets of flour + packets of cinnamon Total packets = 24 + 144 + 18 Total packets = <<24+144+18=186>>186 packets Therefore, the bakery will have a total of 186 packets of ingredients after dividing them according to the recipe. #### 186

Min-ju is the coach of the Seoul Slammers, a Korean youth basketball team. They are preparing for a tournament and need to optimize their strategy. Each game is divided into four quarters, and the team has a different scoring average for each quarter: 15 points in the first quarter, 20 points in the second quarter, 18 points in the third quarter, and 12 points in the fourth quarter. However, the team's point guard, Ji-hoon, has a special play that can increase their scoring average by 3 points in any one quarter of the game. In which quarter should Ji-hoon use his special play to maximize the team's total score?

To maximize the team's total score, we need to determine in which quarter Ji-hoon should use his special play. Let's analyze the scoring averages for each quarter and calculate the potential increase in each quarter. 1. First quarter: The team averages 15 points. If Ji-hoon uses his special play, they could score an average of 15 + 3 = <<15+3=18>>18 points. 2. Second quarter: The team averages 20 points. With the special play, they could score an average of 20 + 3 = <<20+3=23>>23 points. 3. Third quarter: The team averages 18 points. With the special play, they could score an average of 18 + 3 = <<18+3=21>>21 points. 4. Fourth quarter: The team averages 12 points. With the special play, they could score an average of 12 + 3 = <<12+3=15>>15 points. Now, let's calculate the potential total score for each scenario: - Using the special play in the first quarter: 18 + 20 + 18 + 12 = <<18+20+18+12=68>>68 points. - Using the special play in the second quarter: 15 + 23 + 18 + 12 = <<15+23+18+12=68>>68 points. - Using the special play in the third quarter: 15 + 20 + 21 + 12 = <<15+20+21+12=68>>68 points. - Using the special play in the fourth quarter: 15 + 20 + 18 + 15 = <<15+20+18+15=68>>68 points. However, we need to identify the highest increase. The highest increase happens when the special play is used in the quarter with the highest scoring average because that creates the highest potential additional points. Among the options, using the special play in the second quarter offers the highest potential scoring average (23 points), making it the best choice for maximizing the team's total score, even though the total score calculation seems the same for all quarters. #### 2

Minh spends 25% of her monthly allowance on painting supplies and 30% on materials for her handmade crafts. If she spends $15 more on painting supplies than on materials for her crafts, and her total allowance is $200, how much does she spend on painting supplies?

Let's break this down step by step: 1. Minh's total allowance is $200. 2. She spends 25% of her allowance on painting supplies and 30% on materials for her handmade crafts. 3. Let's denote the amount spent on painting supplies as P and the amount spent on materials for her crafts as C. 4. We are given that P = C + $15. 5. From the percentages given, we can set up the equation: P + C = 0.25*200 + 0.30*200 = 0.55*200. <<0.25*200=50>> <<0.30*200=60>> <<0.55*200=110>> Therefore, P + C = $110. 6. Substitute P from step 4 into the equation from step 5: C + $15 + C = $110. Simplifying gives us: 2C + $15 = $110. Subtract $15 from both sides: 2C = $95. <<110-15=95>> 7. Divide by 2 to solve for C: C = $47.50. <<95/2=47.5>> 8. Since P = C + $15, we substitute the value of C: P = $47.50 + $15 = $62.50. Therefore, Minh spends $62.50 on painting supplies. #### 62.50

Fatima has 15 birds in her backyard aviary. She receives 7 more birds as gifts from her friends. If she then releases 3 birds into the wild, how many birds does Fatima have left in her aviary?

Let's solve this step by step: 1. Fatima starts with 15 birds in her backyard aviary. 2. She receives 7 more birds as gifts from her friends, so we add these to the initial number of birds: <<15 + 7 = 22>> 3. Now, Fatima has 22 birds in her aviary. 4. She releases 3 birds into the wild, so we subtract these from the total number of birds: <<22 - 3 = 19>> Therefore, Fatima has 19 birds left in her aviary. #### 19

Lupita's abuela invested $500 in a savings account with a 4% annual interest rate compounded annually. If the interest is compounded for 3 years, how much will Lupita's abuela have in total after the 3 years?

To find the total amount Lupita's abuela will have after 3 years, we'll calculate the amount after each year, using the formula for compound interest: A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate (in decimal), and n is the number of years. 1. Convert the annual interest rate to decimal: 4% = 0.04. 2. Calculate the amount after the first year: A1 = 500(1 + 0.04)^1 = 500 * 1.04 = <<500 * 1.04 = 520>>520 3. Calculate the amount after the second year: A2 = 520(1 + 0.04)^1 = 520 * 1.04 = <<520 * 1.04 = 540.8>>540.8 4. Calculate the amount after the third year: A3 = 540.8(1 + 0.04)^1 = 540.8 * 1.04 = <<540.8 * 1.04 = 562.432>>562.43 Therefore, after rounding to two decimal places, Lupita's abuela will have a total of $562.43 after 3 years. #### 562.43

Nguyễn Thị Mai is analyzing the attendance record of her class. The record shows that 15 students were absent on Monday, 8 students on Tuesday, and 12 students on Wednesday. If there are 40 students in her class, what is the average number of students present over the three days?

Let's break down the steps to find the average number of students present: 1. First, calculate the total number of students absent over the three days: Monday: 15 students, Tuesday: 8 students, Wednesday: 12 students Total absent = 15 + 8 + 12 = <<15+8+12=35>>35 students 2. Since there are 40 students in the class, we can find the total number of students present over the three days: Total present = Total number of students * Number of days - Total absent Total present = 40 * 3 - 35 = <<40*3-35=85>>85 students 3. To find the average number of students present, divide the total present by the number of days: Average present = Total present / Number of days Average present = 85 / 3 = <<85/3=28.33>>28.33 students Therefore, the average number of students present over the three days is 28.33. #### 28.33

Amira is planning a road trip from Cairo to Alexandria. If the distance between the two cities is 220 kilometers and her car's fuel efficiency is 12 kilometers per liter, how many liters of fuel will she need for the trip if she also plans to drive 15% of the distance in the city, where her car's fuel efficiency drops to 8 kilometers per liter?

Let's solve this step-by-step: 1. First, calculate the total distance of the trip: The distance between Cairo and Alexandria is 220 kilometers. 2. Calculate the distance driven in the city: 15% of 220 kilometers = <<15/100 * 220 = 33>> kilometers in the city. 3. Calculate the distance driven outside the city: 220 kilometers - 33 kilometers = <<220 - 33 = 187>> kilometers outside the city. 4. Calculate the fuel needed for the city part of the trip: Distance in the city / Fuel efficiency in the city = 33 kilometers / 8 kilometers per liter = <<33/8 = 4.125>> liters. 5. Calculate the fuel needed for the outside city part of the trip: Distance outside the city / Fuel efficiency outside the city = 187 kilometers / 12 kilometers per liter = <<187/12 = 15.5833>> liters. 6. Calculate the total fuel needed for the trip: Fuel needed for the city part + Fuel needed for the outside city part = 4.125 liters + 15.5833 liters = <<4.125 + 15.5833 = 19.7083>> liters. Therefore, Amira will need approximately 19.7083 liters of fuel for the trip, rounding to two decimal places gives 19.71 liters. #### 19.71

Min-ju's parents gave her 500,000 won on her last birthday, which she deposited into a savings account that earns a 2% annual interest rate compounded annually. If Min-ju doesn't make any withdrawals, how much money will she have in her account after 5 years?

To find out how much money Min-ju will have in her account after 5 years, we need to calculate the compound interest. Here's how we can do it step by step: 1. First, we need to understand the formula for compound interest, which is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial amount of money), r is the annual interest rate (in decimal form), and n is the number of years the money is invested for. 2. In this case, the principal amount (P) is 500,000 won, the annual interest rate (r) is 2%, or 0.02 in decimal form, and the number of years (n) is 5. 3. We will use the formula A = 500,000(1 + 0.02)^5 to calculate the amount of money Min-ju will have in her account after 5 years. 4. Calculate the value inside the parentheses first: 1 + 0.02 = <<1 + 0.02 = 1.02>> 5. Now, raise 1.02 to the power of 5: 1.02^5 = <<1.02^5 = 1.104080803>> 6. Multiply the principal amount by this value to get the total amount after 5 years: 500,000 * 1.104080803 = <<500000 * 1.104080803 = 552040.4015>> 7. Therefore, after 5 years, Min-ju will have approximately 552,040.40 won in her account. #### 552040.40

Ayşe, a teacher at a Turkish high school, has 15 boxes of pencils to distribute among 5 classrooms. Each box contains 24 pencils. How many pencils will each classroom receive if the pencils are divided evenly?

Let's solve this step by step: 1. First, we need to find the total number of pencils Ay\u015fe has. Since she has 15 boxes, and each box contains 24 pencils, we multiply the number of boxes by the number of pencils per box: <<15 * 24 = 360>> So, Ay\u015fe has 360 pencils in total. 2. Next, we need to divide these pencils evenly among 5 classrooms. To find out how many pencils each classroom will receive, we divide the total number of pencils by the number of classrooms: <<360 / 5 = 72>> Therefore, each classroom will receive 72 pencils. #### 72

Luana is building a miniature replica of the iconic Brazilian statue, Christ the Redeemer. She needs to paint the statue and its base. The base requires 2 coats of paint, and each coat needs 250ml of paint. The statue itself needs 3 coats, with each coat requiring 150ml of paint. How many milliliters of paint will Luana need in total to complete the project?

Let's solve this step-by-step: 1. Calculate the total paint needed for the base: Each coat needs 250ml of paint, and there are 2 coats. Total paint for the base = 2 * 250ml = <<2*250=500>>500ml 2. Calculate the total paint needed for the statue: Each coat needs 150ml of paint, and there are 3 coats. Total paint for the statue = 3 * 150ml = <<3*150=450>>450ml 3. Add the paint needed for the base and the statue to find the total: Total paint needed = 500ml + 450ml = <<500+450=950>>950ml Therefore, Luana will need 950 milliliters of paint in total to complete the project. #### 950

Fatima is building a large-scale model of the Burj Khalifa for a school project. She has 36 packs of identical building blocks, each containing 15 blocks. If she uses 3/5 of the blocks for the base and the rest for the tower, and she wants the tower to be 4 times as tall as the base, how many blocks tall can she make the tower?

Let's solve this step by step: 1. First, calculate the total number of blocks Fatima has: 36 packs * 15 blocks/pack = <<36 * 15 = 540>>540 blocks 2. Determine how many blocks she will use for the base and the tower: Blocks for the base = 3/5 * 540 = <<3/5 * 540 = 324>>324 blocks Blocks for the tower = 540 - 324 = <<540 - 324 = 216>>216 blocks 3. Since the tower is 4 times as tall as the base, we can express the height of the tower in terms of the base height: Let's denote the height of the base as B and the height of the tower as T. T = 4B 4. We also know that the total number of blocks used for the tower and the base must add up to the total blocks available for these parts: 3/5 * 540 + 4B = 540 5. However, this equation does not correctly represent the distribution of blocks to the height of the tower and base directly. We need to find the actual height based on the blocks used for the tower since we know the tower's block count and its proportional height to the base. Given that we want to find the height in blocks for the tower and we know the tower's block count (216 blocks), we can directly use this information for the height calculation since each block represents a unit of height in this context. 6. Calculate the height of the tower using the blocks assigned for the tower: Since each block represents one unit of height, the height of the tower in blocks is simply the number of blocks used for the tower. Therefore, the height of the tower = 216 blocks 7. The problem specifically asks for the height of the tower, so our calculation directly gives us the answer we need without further conversion. Therefore, Fatima can make the tower 216 blocks tall. #### 216

Ahmed is planning a camping trip in the desert with his friends. They want to set up a rectangular campsite with an area of 240 square meters. If the length of the campsite is 4 meters more than its width, what is the perimeter of the campsite in meters?

Let's solve this step by step: 1. Define the variables: Let w be the width of the campsite in meters. Since the length is 4 meters more than the width, the length can be represented as (w + 4) meters. 2. The area of a rectangle is given by the formula Area = length * width. We are given that the area is 240 square meters. So, we can write the equation: w * (w + 4) = 240. 3. Expand the equation: w^2 + 4w = 240. 4. Rearrange the equation to form a quadratic equation: w^2 + 4w - 240 = 0. 5. Solve the quadratic equation for w using the quadratic formula or by factoring. The quadratic equation can be factored as (w + 20)(w - 12) = 0. This gives us two possible values for w: w = -20 (not possible since width cannot be negative) or w = 12. 6. Since the width is 12 meters, the length is 12 + 4 = <<12 + 4 = 16>>16 meters. The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(16 + 12) = 2 * 28 = <<2 * 28 = 56>>56 meters. Therefore, the perimeter of the campsite is 56 meters. #### 56

Mei Ling observes a group of birds in the Shanghai Botanical Garden, where the ratio of male birds to female birds is 3:5. If she counts a total of 24 male birds, how many female birds are there?

To find the number of female birds, let's use the given ratio and the total number of male birds Mei Ling observed. 1. The ratio of male birds to female birds is 3:5. This means for every 3 male birds, there are 5 female birds. 2. Mei Ling counted a total of 24 male birds. To find the number of female birds, we first need to figure out the multiplier used to scale up from the ratio to the actual count of male birds. We do this by dividing the actual count of male birds by the ratio's value for male birds: 24 male birds / 3 male birds in the ratio = <<24/3=8>>8 This multiplier is 8. 3. Now, we use this multiplier to find the number of female birds by multiplying it by the ratio's value for female birds: 5 female birds in the ratio * 8 = <<5*8=40>>40 female birds Therefore, there are 40 female birds in the group Mei Ling observed. #### 40

Takashi is the captain of his school's archery team in Tokyo. In an upcoming competition, he has to hit the target 3 times in a row to win. His probability of hitting the target on the first shot is 0.7, but it increases by 10% for each subsequent shot if he hits the previous one. If Takashi misses a shot, his probability of hitting the target on the next shot decreases to 0.4. What is the probability that Takashi will win the competition?

To solve this problem, we'll break it down step by step: 1. Takashi's probability of hitting the target on the first shot is 0.7. 2. If he hits the target on the first shot, his probability of hitting it on the second shot increases by 10%, making it 0.7 + 0.1 = <<0.7 + 0.1 = 0.8>>. 3. If he hits the target on the second shot, his probability of hitting it on the third shot increases by another 10%, making it 0.8 + 0.1 = <<0.8 + 0.1 = 0.9>>. 4. The probability that Takashi hits the target three times in a row is the product of the probabilities of each shot: 0.7 * 0.8 * 0.9 = <<0.7 * 0.8 * 0.9 = 0.504>>. However, we also need to account for the scenario where Takashi misses a shot. If he misses the first shot, his probability of winning is 0, since he has to hit three times in a row. If he hits the first shot but misses the second, his probability of winning is also 0 for the same reason. Therefore, the only scenario where Takashi can win if he misses a shot is if he hits the first two shots but misses the third. The probability of this happening is 0.7 * 0.8 * 0.1 = <<0.7 * 0.8 * 0.1 = 0.056>> (since his probability of missing the third shot is 1 - 0.9 = 0.1). However, since we are looking for the probability of Takashi winning, we do not consider the scenario where he misses the third shot. Hence, we only consider the first scenario where he hits all three shots. Thus, the overall probability of Takashi winning is the probability of him hitting three times in a row, which is 0.504. #### 0.504

Rohan is planning a road trip from Mumbai to Delhi, a distance of 1,400 kilometers. If his car's fuel tank can hold 50 liters of petrol and the car's mileage is 14 kilometers per liter, how many times will Rohan need to refill his tank during the trip?

Let's break down the problem step by step: 1. First, we need to find out how many kilometers Rohan's car can travel on a full tank of petrol: The car's mileage is 14 kilometers per liter, and the tank holds 50 liters of petrol, so the distance it can travel on a full tank is: 50 liters * 14 kilometers/liter = <<50*14=700>>700 kilometers 2. Now, we need to determine how many times Rohan needs to refill his tank to cover the total distance of 1,400 kilometers: To find this out, we'll divide the total distance by the distance the car can travel on a full tank: 1,400 kilometers / 700 kilometers = <<1400/700=2>>2 Therefore, Rohan will need to refill his tank 2 times during the trip. #### 2

Kofi invests 500 Ghanaian cedis in a crafting business that earns a 5% annual interest rate compounded annually. If he doesn't withdraw any money, how much will he have after 6 years?

To find out how much Kofi will have after 6 years, we need to calculate the compound interest earned on his initial investment of 500 Ghanaian cedis at a 5% annual interest rate compounded annually. 1. First, let's convert the annual interest rate to a decimal: 5% = 0.05. 2. The formula for compound interest is A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate, and n is the number of years. 3. Plugging in the values, we get A = 500(1 + 0.05)^6. 4. Calculate the value inside the parentheses first: (1 + 0.05) = <<1 + 0.05 = 1.05>>. 5. Raise 1.05 to the power of 6 to find the factor by which the initial investment grows: 1.05^6 = <<1.05^6 = 1.3382255776>>. 6. Multiply the initial investment by this growth factor to find the total amount after 6 years: 500 * 1.3382255776 = <<500 * 1.3382255776 = 669.1127888>>. Therefore, Kofi will have approximately 669.11 Ghanaian cedis after 6 years. #### 669.11

Fatima bought a new smartphone for 2500 AED. The phone's value depreciates by 20% every year. If she decides to sell the phone after 3 years, how much will she get for it, assuming she also has to pay a 5% commission to the salesperson?

Let's solve this step by step: 1. First, calculate the depreciation of the phone's value after the first year: Depreciation = 20% of 2500 AED = <<20/100 * 2500 = 500>>AED Value after 1 year = 2500 - 500 = <<2500 - 500 = 2000>>AED 2. Calculate the depreciation of the phone's value after the second year: Depreciation = 20% of 2000 AED = <<20/100 * 2000 = 400>>AED Value after 2 years = 2000 - 400 = <<2000 - 400 = 1600>>AED 3. Calculate the depreciation of the phone's value after the third year: Depreciation = 20% of 1600 AED = <<20/100 * 1600 = 320>>AED Value after 3 years = 1600 - 320 = <<1600 - 320 = 1280>>AED 4. Calculate the commission paid to the salesperson: Commission = 5% of 1280 AED = <<5/100 * 1280 = 64>>AED 5. Calculate the amount Fatima will get after paying the commission: Amount = 1280 - 64 = <<1280 - 64 = 1216>>AED Therefore, Fatima will get 1216 AED for her phone after 3 years. #### 1216

The Wildcats basketball team has played 15 games so far this season, with an average score of 72 points per game. In their last 5 games, they scored 80, 78, 70, 85, and 75 points. If they want to maintain an average score of at least 75 points per game for the entire season, what is the minimum total score they need to achieve in their next 5 games?

To find the minimum total score the Wildcats need in their next 5 games, let's break it down step by step: 1. First, calculate the total points scored in the first 15 games: Since the average score for 15 games is 72 points, the total points scored so far is: Total points in 15 games = 72 * 15 = <<72*15=1080>>1080 points 2. Next, calculate the total points scored in the last 5 games: Total points in last 5 games = 80 + 78 + 70 + 85 + 75 = <<80+78+70+85+75=388>>388 points 3. Now, calculate the total points scored in the first 10 games (excluding the last 5 games): Total points in first 10 games = Total points in 15 games - Total points in last 5 games Total points in first 10 games = 1080 - 388 = <<1080-388=692>>692 points 4. The team wants to maintain an average of at least 75 points per game for the entire season (20 games). Calculate the minimum total points required for the entire season: Minimum total points required = 75 * 20 = <<75*20=1500>>1500 points 5. Since the team already has 1080 points, calculate the minimum additional points needed for the next 5 games to reach the target: Minimum points needed in next 5 games = Minimum total points required - Total points in 15 games Minimum points needed in next 5 games = 1500 - 1080 = <<1500-1080=420>>420 points 6. Therefore, the minimum total score the Wildcats need in their next 5 games to maintain an average score of at least 75 points per game for the entire season is 420 points. #### 420

Ayşe is building a miniature Ottoman-style mosque using balsa wood and paint. She wants to apply a 15% discount to the total cost of materials, which is 500 Turkish Lira. However, she also needs to add an 8% tax on the discounted price. How much will Ayşe pay in total for the materials after the discount and tax are applied?

Let's solve this step by step: 1. First, calculate the discount amount: Discount = 15% of 500 Turkish Lira = <<15/100 * 500 = 75>>75 Turkish Lira 2. Calculate the price after the discount: Price after discount = Total cost - Discount = 500 - 75 = <<500 - 75 = 425>>425 Turkish Lira 3. Calculate the tax amount on the discounted price: Tax = 8% of 425 Turkish Lira = <<8/100 * 425 = 34>>34 Turkish Lira 4. Calculate the total price after adding the tax: Total price = Price after discount + Tax = 425 + 34 = <<425 + 34 = 459>>459 Turkish Lira Therefore, Ay\u015fe will pay 459 Turkish Lira in total for the materials after the discount and tax are applied. #### 459

Rohan's school is experiencing a rapid increase in student enrollment. In 2018, there were 500 students, and the enrollment has been growing at a rate of 15% each year. If this growth rate continues, how many students will Rohan's school have in 2023?

Let's break this down step by step: 1. First, calculate the growth rate as a decimal: 15% = <<15/100=0.15>>0.15. 2. Calculate the number of years from 2018 to 2023: 2023 - 2018 = <<2023-2018=5>>5 years. 3. Apply the exponential growth formula: Students in 2023 = 500 * (1 + 0.15)^5 = 500 * (1.15)^5 = 500 * <<(1.15)^5=2.0113571875>>2.0113571875 = 1005.67859375. Rounding to the nearest whole number, as students must be whole individuals, we get: 1006 students. #### 1006

The Wong family is planning a reunion dinner at a Chinese restaurant. The ratio of adults to children is 5:3. If there are 15 adults attending, and the total cost of the dinner is $480, what is the cost per person if the children's meals are half the price of the adults'?

Let's solve this step by step: 1. First, we need to find the number of children attending the dinner. Since the ratio of adults to children is 5:3, and there are 15 adults, we can set up a proportion to find the number of children: 5/3 = 15/x Cross-multiplying: 5x = 3 * 15 5x = <<3 * 15 = 45>> Dividing both sides by 5: x = 45 / 5 x = <<45 / 5 = 9>> children 2. Now, we know there are 15 adults and 9 children. Let's denote the cost of an adult meal as A and the cost of a child meal as C. We are told that C = A / 2. The total cost of the dinner is $480, so we can set up an equation based on the number of adults and children: 15A + 9C = 480 Since C = A / 2, we substitute C in the equation: 15A + 9(A / 2) = 480 Multiplying everything by 2 to get rid of the fraction: 30A + 9A = 960 Combining like terms: 39A = 960 Solving for A: A = 960 / 39 A = <<960 / 39 = 24.6154>> (approximately) 3. Now that we know the cost of an adult meal (A), we can find the cost of a child meal (C): C = A / 2 = 24.6154 / 2 C = <<24.6154 / 2 = 12.3077>> (approximately) To find the total cost per person, we need to calculate the total number of people and divide the total cost by this number: Total number of people = 15 adults + 9 children = <<15 + 9 = 24>> Total cost per person = Total cost / Total number of people = 480 / 24 Total cost per person = <<480 / 24 = 20>> Therefore, the cost per person is approximately $20. #### 20

Amira is building a miniature mosque for a school project. She needs to increase the size of the original blueprint by 15% to make it more visible. If the original blueprint is 30 cm in length and 20 cm in width, what will be the new dimensions of the blueprint after the increase, and what will be the new area in square centimeters?

To find the new dimensions and area of the blueprint, we'll follow these steps: 1. Calculate the increase in length: The original length is 30 cm, and it needs to be increased by 15%. First, find 15% of 30 cm: 15% of 30 cm = (15/100) * 30 cm = <<15/100*30=4.5>>4.5 cm Then, add this increase to the original length to find the new length: New length = original length + increase = 30 cm + 4.5 cm = <<30+4.5=34.5>>34.5 cm 2. Calculate the increase in width: The original width is 20 cm, and it needs to be increased by 15%. First, find 15% of 20 cm: 15% of 20 cm = (15/100) * 20 cm = <<15/100*20=3>>3 cm Then, add this increase to the original width to find the new width: New width = original width + increase = 20 cm + 3 cm = <<20+3=23>>23 cm 3. Calculate the new area: The area of a rectangle (such as the blueprint) is found by multiplying its length by its width. New area = new length * new width = 34.5 cm * 23 cm = <<34.5*23=793.5>>793.5 square cm Therefore, the new dimensions of the blueprint are 34.5 cm in length and 23 cm in width, and the new area is 793.5 square cm. #### 793.5

Maya is planning a Canadian Thanksgiving dinner for her family and wants to make a traditional tourtière. The recipe she found serves 8 people and requires a ratio of 5 parts ground pork to 3 parts ground beef. If she needs to feed 12 people, how many kilograms of each type of meat should she buy if she wants to maintain the same ratio and the original recipe calls for 1.5 kg of ground pork and 0.9 kg of ground beef?

To solve this, we'll follow these steps: 1. Calculate the total amount of meat needed for 8 people using the original recipe: Total meat for 8 people = Ground pork + Ground beef = 1.5 kg + 0.9 kg = <<1.5 + 0.9 = 2.4>>2.4 kg 2. Determine the ratio of total meat to the number of people in the original recipe: Ratio = Total meat / Number of people = 2.4 kg / 8 people = <<2.4 / 8 = 0.3>>0.3 kg/person 3. Calculate the total amount of meat needed for 12 people to maintain the ratio: Total meat for 12 people = Ratio * Number of people = 0.3 kg/person * 12 people = <<0.3 * 12 = 3.6>>3.6 kg 4. Since the ratio of ground pork to ground beef is 5:3, calculate the portion of the total meat that should be ground pork: Fraction of ground pork = 5 / (5 + 3) = 5 / 8 = <<5 / 8 = 0.625>>0.625 5. Calculate the amount of ground pork needed for 12 people: Ground pork for 12 people = Total meat for 12 people * Fraction of ground pork = 3.6 kg * 0.625 = <<3.6 * 0.625 = 2.25>>2.25 kg 6. Calculate the amount of ground beef needed for 12 people, given the total meat and the amount of ground pork: Ground beef for 12 people = Total meat for 12 people - Ground pork for 12 people = 3.6 kg - 2.25 kg = <<3.6 - 2.25 = 1.35>>1.35 kg Therefore, Maya should buy 2.25 kg of ground pork and 1.35 kg of ground beef. #### 3.6

Maria is building a scale model of a Spanish galleon for a local museum exhibit. The model's hull will be 3/5 the length of the original ship, which was 120 feet long. If the original ship had a beam (width) that was 1/3 of its length, and Maria wants to maintain the same proportions in her model, what will be the beam of her model ship in feet?

To find the beam of Maria's model ship, we'll follow these steps: 1. Determine the length of the model ship's hull, which is 3/5 of the original ship's length: Length of model hull = 3/5 * 120 feet = <<3/5*120=72>>72 feet 2. Calculate the beam of the original ship, which is 1/3 of its length: Beam of original ship = 1/3 * 120 feet = <<1/3*120=40>>40 feet 3. Since Maria wants to maintain the same proportions, the beam of her model ship will be 3/5 of the original ship's beam, just like the length: Beam of model ship = 3/5 * 40 feet = <<3/5*40=24>>24 feet Therefore, the beam of Maria's model ship will be 24 feet. #### 24

Kanchana and her friends are planning a camping trip in the mountains of Chiang Mai. They want to set up their tents in a rectangular area with an area of 240 square meters. If the length of the area is 4 meters more than its width, what should be the dimensions of the rectangular area to accommodate all their tents?

To find the dimensions of the rectangular area, let's denote the width as w and the length as l. We're given that the length is 4 meters more than the width, so we can express the length in terms of the width as l = w + 4. The area of a rectangle is given by the formula A = length * width. We're told the area is 240 square meters, so we can set up the equation: w * (w + 4) = 240 Expanding the equation, we get: w^2 + 4w = 240 Rearranging the equation to set it to 0 gives us: w^2 + 4w - 240 = 0 Now, we can solve for w using the quadratic formula: w = (-b ± √(b^2 - 4ac)) / 2a In our case, a = 1, b = 4, and c = -240. Plugging these values into the formula gives us: w = (-(4) ± √((4)^2 - 4*1*(-240))) / 2*1 w = (-4 ± √(16 + 960)) / 2 w = (-4 ± √976) / 2 w = (-4 ± 31.23) / 2 We have two possible solutions for w, but since width cannot be negative, we take the positive solution: w = (-4 + 31.23) / 2 w = <<27.23 / 2 = 13.615>> meters Since the length is 4 meters more than the width: l = w + 4 l = 13.615 + 4 l = <<13.615 + 4 = 17.615>> meters Therefore, the dimensions of the rectangular area should be approximately 13.62 meters by 17.62 meters to accommodate all their tents. #### 17.62

Fatima is observing the bird population in a nature reserve in Dubai. The population of a specific species of bird increases by 15% every year. If there are currently 200 birds, how many will there be in 4 years?

To solve this, let's break it down into steps: 1. First, we understand that the bird population increases by 15% each year. This means we can calculate the population increase each year as 15% of the current population and then add it to the current population to get the new population. 2. The formula to calculate the increase is: Increase = Current Population * 15% (or 0.15 when expressed as a decimal). 3. The formula to calculate the new population each year is: New Population = Current Population + Increase. Let's apply this step by step for each year: - Year 1: Increase = 200 * 0.15 = <<200 * 0.15 = 30>> New Population = 200 + 30 = <<200 + 30 = 230>> - Year 2: Increase = 230 * 0.15 = <<230 * 0.15 = 34.5>> New Population = 230 + 34.5 = <<230 + 34.5 = 264.5>> - Year 3: Increase = 264.5 * 0.15 = <<264.5 * 0.15 = 39.675>> New Population = 264.5 + 39.675 = <<264.5 + 39.675 = 304.175>> - Year 4: Increase = 304.175 * 0.15 = <<304.175 * 0.15 = 45.62625>> New Population = 304.175 + 45.62625 = <<304.175 + 45.62625 = 349.80125>> Therefore, after 4 years, there will be approximately 349.80 birds, rounding to two decimal places for practical purposes. #### 349.80

A wildlife conservation organization in Canada wants to create a fund to support the protection of endangered beavers. They deposit $5,000 into an account with a 4% annual interest rate, compounded annually. If they add $1,000 to the account every year, how much will they have in the account after 6 years to support the conservation efforts?

Let's solve this step-by-step: 1. The initial deposit is $5,000. 2. The annual interest rate is 4%, compounded annually, meaning the interest is applied once per year. This is represented by the formula A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), and n is the number of years. 3. Each year, $1,000 is added to the account. We'll calculate the total amount in the account after each year, considering both the interest and the additional deposit. Year 1: - Interest: $5,000 * 4% = $5,000 * 0.04 = <<5000 * 0.04 = 200>>$200 - Total after interest: $5,000 + $200 = <<5000 + 200 = 5200>>$5,200 - Adding the $1,000 deposit: $5,200 + $1,000 = <<5200 + 1000 = 6200>>$6,200 Year 2: - Interest: $6,200 * 4% = $6,200 * 0.04 = <<6200 * 0.04 = 248>>$248 - Total after interest: $6,200 + $248 = <<6200 + 248 = 6448>>$6,448 - Adding the $1,000 deposit: $6,448 + $1,000 = <<6448 + 1000 = 7448>>$7,448 Year 3: - Interest: $7,448 * 4% = $7,448 * 0.04 = <<7448 * 0.04 = 297.92>>$297.92 - Total after interest: $7,448 + $297.92 = <<7448 + 297.92 = 7745.92>>$7,745.92 - Adding the $1,000 deposit: $7,745.92 + $1,000 = <<7745.92 + 1000 = 8745.92>>$8,745.92 Year 4: - Interest: $8,745.92 * 4% = $8,745.92 * 0.04 = <<8745.92 * 0.04 = 349.8368>>$349.84 - Total after interest: $8,745.92 + $349.84 = <<8745.92 + 349.84 = 9095.76>>$9,095.76 - Adding the $1,000 deposit: $9,095.76 + $1,000 = <<9095.76 + 1000 = 10095.76>>$10,095.76 Year 5: - Interest: $10,095.76 * 4% = $10,095.76 * 0.04 = <<10095.76 * 0.04 = 403.8304>>$403.83 - Total after interest: $10,095.76 + $403.83 = <<10095.76 + 403.83 = 10499.59>>$10,499.59 - Adding the $1,000 deposit: $10,499.59 + $1,000 = <<10499.59 + 1000 = 11499.59>>$11,499.59 Year 6: - Interest: $11,499.59 * 4% = $11,499.59 * 0.04 = <<11499.59 * 0.04 = 459.9836>>$459.98 - Total after interest: $11,499.59 + $459.98 = <<11499.59 + 459.98 = 11959.57>>$11,959.57 - Adding the $1,000 deposit: $11,959.57 + $1,000 = <<11959.57 + 1000 = 12959.57>>$12,959.57 Therefore, after 6 years, the organization will have $12,959.57 in the account to support the conservation efforts. #### 12959.57

Aisha is preparing a traditional West African dish, jollof rice, for a large family gathering. The recipe serves 8 people and requires a ratio of 2 cups of rice to 3 cups of water. If Aisha wants to serve 24 people, and she already has 12 cups of water, how many cups of rice should she use?

To solve this problem, we need to first find out how many times Aisha needs to multiply the recipe to serve 24 people. Since the original recipe serves 8 people, we can find this by dividing 24 by 8: 24 ÷ 8 = <<24/8=3>>3. This means Aisha needs to triple the recipe. Next, we need to determine the total amount of water needed for the tripled recipe. The original recipe requires 3 cups of water for 8 people. For 24 people, we multiply this by 3: 3 cups * 3 = <<3*3=9>>9 cups. However, Aisha already has 12 cups of water, which is more than needed. Since the ratio of rice to water is 2:3, and we know the amount of water needed for the tripled recipe is 9 cups, we can set up a proportion to find the amount of rice needed: 2/3 = x/9, where x is the amount of rice. Cross-multiplying gives us 3x = 2*9, so 3x = 18. Dividing both sides by 3, we find x = 18/3 = <<18/3=6>>6 cups of rice. Therefore, Aisha should use 6 cups of rice for the tripled recipe to serve 24 people. #### 6

The five friends want to split the total cost evenly. If they each contribute the same amount, how much will each friend pay?

To determine how much each friend will pay, we need to know the total cost they are splitting. Since the total cost isn't provided, let's assign a variable to represent it, but for the purpose of providing a numeric answer, we'll have to give an example total cost. Let's say the total cost for this example is $1000. 1. First, we identify the total cost that needs to be split: $1000. 2. Since there are five friends, we divide the total cost by the number of friends to find out how much each will pay: $1000 ÷ 5 = <<1000 / 5 = 200>>. Therefore, if the total cost were $1000, each friend would pay $200. #### 200

Rohan is planning a road trip from Mumbai to Delhi, covering a distance of 1,400 km. His car's fuel efficiency is 15 km per liter, and the fuel price is 80 rupees per liter. If Rohan wants to budget his fuel expenses, how much should he allocate for the entire trip, considering a 5% increase in fuel prices due to taxes?

To solve this problem, we'll break it down into steps: 1. First, we need to calculate how much fuel Rohan's car will consume for the entire trip. Given the car's fuel efficiency is 15 km per liter, we divide the total distance by the fuel efficiency: Fuel consumption = Total distance / Fuel efficiency = 1400 km / 15 km/liter = <<1400 / 15 = 93.33>>93.33 liters 2. Next, we calculate the fuel cost without the tax increase: Fuel cost without tax increase = Fuel consumption * Fuel price per liter = 93.33 liters * 80 rupees/liter = <<93.33 * 80 = 7466.4>>7466.4 rupees 3. Then, we calculate the additional cost due to the 5% tax increase: Tax increase amount = 5% of Fuel cost without tax increase = 0.05 * 7466.4 rupees = <<0.05 * 7466.4 = 373.32>>373.32 rupees 4. Finally, we find the total fuel cost including the tax increase: Total fuel cost = Fuel cost without tax increase + Tax increase amount = 7466.4 rupees + 373.32 rupees = <<7466.4 + 373.32 = 7839.72>>7839.72 rupees Therefore, Rohan should allocate 7839.72 rupees for fuel expenses for the entire trip. #### 7839.72

Mia is planning a camping trip in the Canadian Rockies and has a budget of $800 for equipment. She buys a tent for $120, which is 15% off the original price. She then purchases a sleeping bag for $80, which is 20% off. If she also needs to buy a backpack and a portable stove, and the total cost of these two items is $180, what percentage of her budget will she have left after all the purchases?

Let's break down Mia's expenses step by step to find out what percentage of her budget she'll have left. 1. First, calculate the original price of the tent before the 15% discount: Let x be the original price of the tent. Since the discount is 15%, the price Mia paid is 85% of the original price: 85% of x = $120 To find x, convert the percentage to a decimal and solve for x: 0.85x = 120 x = 120 / 0.85 x = <<120 / 0.85 = 141.18>> So, the original price of the tent was approximately $141.18. 2. Next, calculate the original price of the sleeping bag before the 20% discount: Let y be the original price of the sleeping bag. Since the discount is 20%, the price Mia paid is 80% of the original price: 80% of y = $80 To find y, convert the percentage to a decimal and solve for y: 0.8y = 80 y = 80 / 0.8 y = <<80 / 0.8 = 100>> So, the original price of the sleeping bag was $100. 3. Now, calculate the total amount Mia spent on the tent and the sleeping bag: Total spent so far = $120 (tent) + $80 (sleeping bag) = <<120 + 80 = 200>> Total spent so far = $200 4. Mia also needs to buy a backpack and a portable stove for a total of $180. Total spent on all items = $200 (previous items) + $180 (backpack and stove) = <<200 + 180 = 380>> Total spent on all items = $380 5. To find the percentage of her budget left, subtract the total amount spent from her budget and divide by her budget, then multiply by 100: Percentage left = ((Budget - Total spent) / Budget) * 100 Percentage left = ((800 - 380) / 800) * 100 Percentage left = (420 / 800) * 100 Percentage left = 0.525 * 100 Percentage left = <<0.525 * 100 = 52.5>>% Therefore, Mia will have 52.5% of her budget left after all the purchases. #### 52.5

Anastasia and her brother Sergei are planning a family dinner in Moscow. They want to make a traditional Russian salad with a ratio of 3 parts beets to 2 parts carrots. If they have 6 cups of beets, how many cups of carrots should they use?

Let's solve this step by step: 1. The ratio of beets to carrots is 3:2, which means for every 3 cups of beets, we need 2 cups of carrots. 2. We have 6 cups of beets, so we need to find out how many cups of carrots are needed to maintain the ratio. 3. To do this, we can set up a proportion using the ratio and the amount of beets we have: 3 cups beets / 2 cups carrots = 6 cups beets / x cups carrots 4. We can then cross-multiply to solve for x: 3x = 6 * 2 3x = <<6 * 2 = 12>> 5. Now, we divide both sides by 3 to find x: x = 12 / 3 x = <<12 / 3 = 4>> 6. Therefore, Anastasia and Sergei should use 4 cups of carrots for their traditional Russian salad. #### 4

Helga wants to create a set of hand-painted ceramic mugs as gifts for her friends. She has 12 hours to devote to this project and it takes her 45 minutes to paint a small mug and 90 minutes to paint a large mug. If she can sell each small mug for €8 and each large mug for €12, how many of each size mug should she paint to maximize her earnings?

Let's break down the solution step by step: 1. First, we need to convert the total available time from hours to minutes because the time to paint each mug is given in minutes: 12 hours * 60 minutes/hour = <<12*60=720>>720 minutes 2. Next, let's denote the number of small mugs as 's' and the number of large mugs as 'l'. We can set up the following equation based on the time constraint: 45s + 90l ≤ 720 3. Since Helga wants to maximize her earnings, we need to set up an equation for her total earnings. Let's denote the price of a small mug as 'p_s' and the price of a large mug as 'p_l'. The total earnings (E) can be calculated as: E = p_s * s + p_l * l Given p_s = €8 and p_l = €12, we substitute these values into the equation: E = 8s + 12l 4. To maximize earnings, we can first find the maximum number of large mugs Helga can paint since they yield a higher profit per unit, then use the remaining time for small mugs. a) If Helga only paints large mugs, the maximum number she can paint is: 720 minutes / 90 minutes/large mug = <<720/90=8>>8 large mugs b) This would leave no time for small mugs. To include small mugs and potentially increase earnings, let's consider reducing the number of large mugs to 7, allowing for some small mugs: Time used for 7 large mugs = 7 * 90 minutes = <<7*90=630>>630 minutes Remaining time for small mugs = 720 minutes - 630 minutes = <<720-630=90>>90 minutes Number of small mugs that can be painted in the remaining time = 90 minutes / 45 minutes/small mug = <<90/45=2>>2 small mugs c) Calculate the total earnings for this combination: E = 8s + 12l E = 8*2 + 12*7 E = 16 + 84 E = <<16+84=100>>100 Therefore, Helga should paint 2 small mugs and 7 large mugs to maximize her earnings. #### 100

Ayşe, a wildlife observer in Turkey, wants to maximize the number of bird species she can spot during a 3-hour observation period at a nature reserve. She has identified three locations to observe birds: Location A, where she can spot 5 species per hour, Location B, where she can spot 3 species per hour, and Location C, where she can spot 4 species per hour. However, she can only spend a maximum of 1 hour at Location A due to restricted access. How many species of birds can Ayşe spot in total if she allocates her time optimally among the three locations?

To maximize the number of bird species Ay\u015fe can spot, we need to allocate her 3-hour observation period optimally among the three locations. Let's break this down step by step: 1. Ay\u015fe can spend a maximum of 1 hour at Location A, where she can spot 5 species per hour. So, the number of species she can spot at Location A is: 5 species/hour * 1 hour = <<5*1=5>>5 species 2. Now, she has 2 hours left to allocate between Location B and Location C. Location B offers 3 species per hour, and Location C offers 4 species per hour. To maximize the number of species, she should spend her remaining time at Location C, as it offers more species per hour. However, we should also consider the scenario where spending time at both B and C could potentially yield more species. 3. Let's calculate the number of species she can spot if she spends her remaining 2 hours at Location C: 4 species/hour * 2 hours = <<4*2=8>>8 species 4. If she spends 1 hour at Location B and 1 hour at Location C, she can spot: 3 species/hour * 1 hour = <<3*1=3>>3 species at Location B, and 4 species/hour * 1 hour = <<4*1=4>>4 species at Location C, for a total of 3 + 4 = <<3+4=7>>7 species. 5. Comparing the two scenarios, spending 2 hours at Location C yields more species (8 species) than splitting her time between Location B and Location C (7 species). 6. So, the optimal allocation of her time is 1 hour at Location A and 2 hours at Location C. 7. The total number of species Ay\u015fe can spot is the sum of the species she can spot at Location A and Location C: 5 species (at Location A) + 8 species (at Location C) = <<5+8=13>>13 species Therefore, Ay\u015fe can spot 13 species of birds in total if she allocates her time optimally among the three locations. #### 13

During the French holiday of Bastille Day, the ratio of adults to children attending a parade in Lyon is 5:3. If 240 adults are present, how many children are attending the parade?

Let's solve this step by step: 1. The ratio of adults to children is 5:3, which means for every 5 adults, there are 3 children. 2. We are given that 240 adults are present. To find the number of children, we need to determine how many groups of 5 adults there are and then calculate the corresponding number of children. 3. Divide the total number of adults by the number of adults per group to find the multiplier for the ratio: 240 adults / 5 adults per group = <<240/5=48>>48 groups 4. Now, multiply the number of groups by the number of children per group to find the total number of children: 48 groups * 3 children per group = <<48*3=144>>144 children Therefore, there are 144 children attending the parade. #### 144

Ayşe is planning a trip from Istanbul to Antalya, Turkey. She wants to visit the ancient city of Perge, which is 15 km east of Antalya. If she takes a flight from Istanbul to Antalya that is 482 km and then drives to Perge, and assuming the flight path is a straight line, what is the total distance Ayşe will travel to get to Perge if she also needs to drive 7 km to get to the airport in Istanbul?

Let's break this down step by step: 1. First, we need to calculate the distance Ayşe travels to get to the airport in Istanbul: The distance to the airport is given as 7 km. 2. Next, we calculate the distance of the flight from Istanbul to Antalya: The flight distance is given as 482 km. 3. Then, we need to find the distance from Antalya to Perge: Perge is 15 km east of Antalya. 4. Now, we add all these distances together to find the total distance Ayşe will travel: Total distance = Distance to the airport + Flight distance + Distance from Antalya to Perge = 7 km + 482 km + 15 km = <<7 + 482 + 15 = 504>>km Therefore, the total distance Ayşe will travel to get to Perge is 504 km. #### 504

During Cinco de Mayo, a Mexican restaurant offers a 15% discount on all orders. If Carlos orders food worth $85, how much will he pay after the discount?

Let's break down the problem step by step: 1. First, we need to calculate the amount of the discount on Carlos' order: The discount is 15% of $85. To find 15% of $85, we multiply $85 by 0.15: $85 * 0.15 = <<85 * 0.15 = 12.75>> So, the discount is $12.75. 2. Now, we subtract the discount from the original price to find the amount Carlos will pay: $85 - $12.75 = <<85 - 12.75 = 72.25>> Therefore, Carlos will pay $72.25 after the discount. #### 72.25

During the Loy Krathong festival in Thailand, Nong's family makes 120 krathongs to sell at the local market. They sell 45 krathongs in the morning and 30 more in the evening. How many krathongs does Nong's family have left to sell the next day?

Let's solve this step-by-step: 1. Nong's family starts with 120 krathongs. 2. They sell 45 krathongs in the morning and 30 more in the evening. To find the total sold, we add the morning and evening sales: <<45 + 30 = 75>> 3. To find out how many krathongs are left, we subtract the total sold from the initial amount: <<120 - 75 = 45>> Therefore, Nong's family has 45 krathongs left to sell the next day. #### 45

Shani is preparing hummus for a family gathering in Tel Aviv. The recipe she found serves 8 people and requires 2 cups of chickpeas, 1/4 cup of tahini, and 1/4 cup of lemon juice. If Shani needs to serve 12 people, how many cups of chickpeas will she need?

To find out how many cups of chickpeas Shani will need, we first need to understand the ratio of servings to the amount of chickpeas in the original recipe. The original recipe serves 8 people and requires 2 cups of chickpeas. 1. Determine the ratio of servings to cups of chickpeas in the original recipe: 8 servings / 2 cups = <<8/2=4>>4 servings per cup. 2. Since Shani needs to serve 12 people, we divide the number of people she needs to serve by the number of servings per cup to find out how many cups she needs: 12 people / 4 servings per cup = <<12/4=3>>3 cups. Therefore, Shani will need 3 cups of chickpeas for 12 people. #### 3

Min-ju is traveling from Seoul to Busan, which is 325 kilometers away. If she takes a train that travels at an average speed of 80 kilometers per hour, how many hours will it take her to reach her destination?

Let's solve this step by step: 1. We need to find the time it takes for Min-ju to travel from Seoul to Busan. 2. The distance between Seoul and Busan is 325 kilometers. 3. The average speed of the train is 80 kilometers per hour. 4. To find the time, we can use the formula: Time = Distance / Speed. 5. Plugging in the values, we get: Time = 325 km / 80 km/h. 6. Now, let's perform the division: <<325 / 80 = 4.0625>> hours. 7. Rounding this value to a more understandable form, we can say it will take approximately 4 hours and 4 minutes. 8. Therefore, it will take Min-ju approximately 4.06 hours to reach her destination. #### 4.06

Rohan is planning a road trip from Mumbai to Delhi. The distance between the two cities is approximately 1,430 kilometers. If his car's fuel efficiency is 12 kilometers per liter and fuel costs 80 rupees per liter, how much will he spend on fuel for the entire trip, assuming he also needs to return to Mumbai?

Let's break this down step by step: 1. First, we need to calculate the total distance Rohan will travel for the round trip: Total distance = Distance from Mumbai to Delhi + Distance from Delhi to Mumbai Since the distance between the two cities is the same in both directions: Total distance = 2 * Distance from Mumbai to Delhi Total distance = 2 * 1430 kilometers = <<2 * 1430 = 2860>>2860 kilometers 2. Next, we calculate how much fuel Rohan's car will consume for the entire trip: Fuel consumption = Total distance / Fuel efficiency Fuel consumption = 2860 kilometers / 12 kilometers per liter = <<2860 / 12 = 238.33>>238.33 liters 3. Now, we find out how much the fuel will cost for the entire trip: Fuel cost = Fuel consumption * Cost per liter Fuel cost = 238.33 liters * 80 rupees per liter = <<238.33 * 80 = 19066.4>>19066.4 rupees 4. Therefore, Rohan will spend approximately 19066.4 rupees on fuel for the entire trip. #### 19066.4

Anh and his friends are setting up a rectangular badminton court in the park. The length of the court is 5 meters more than the width. If the width is 8 meters, what is the area of the badminton court?

To find the area of the badminton court, we first need to determine the length of the court. We know the width is 8 meters and the length is 5 meters more than the width. So, the length can be calculated as follows: Length = Width + 5 = 8 + 5 = <<8+5=13>>13 meters Now that we have the length and width, we can calculate the area of the rectangular badminton court using the formula: Area = Length * Width = 13 * 8 = <<13*8=104>>104 square meters Therefore, the area of the badminton court is 104 square meters. #### 104

Kofi is planning a camping trip in Oyo State with his friends. They want to share some chocolates in a ratio that is the same as the number of hours they will spend hiking to the number of hours they will spend resting. If they plan to hike for 6 hours and rest for 4 hours, and they have 90 chocolates, how many chocolates will Kofi get if he is one of the 5 friends going on the trip?

Let's break this down step by step: 1. First, we need to find the ratio of hours spent hiking to hours spent resting. Given they hike for 6 hours and rest for 4 hours, the ratio is 6:4, which simplifies to 3:2. 2. Since they want to share the chocolates in the same ratio, and there are 5 friends, we need to divide the chocolates into 3 parts + 2 parts = 5 parts in total, maintaining the 3:2 ratio. 3. To find out how many chocolates each part represents, we divide the total chocolates by the total parts (which is the same as the number of friends since the chocolates are being divided among them in the ratio of their activities): Total chocolates = 90 Total parts = 5 (3 parts for hiking + 2 parts for resting) Chocolates per part = <<90 / 5 = 18>> 4. Since Kofi is one of the friends, and assuming each friend gets an equal share based on the activity ratio, we need to find out how many parts Kofi gets. Given the ratio is based on activities and not the number of friends directly, and Kofi is one of the 5 friends participating equally in the activities, he gets 1 part out of the 5 parts. 5. Therefore, Kofi gets 1 part of the chocolates, which we've determined is 18 chocolates per part. #### 18

The question is: At the end of the first semester, Nneoma had an average score of 85 in her mathematics class. In the second semester, she scored 90, 78, and 92 on her first three tests. If she wants to maintain an overall average of at least 87 for the entire year, what is the minimum score she must get on her last test, given that the total number of tests for the year is 8?

To find the minimum score Nneoma needs on her last test, let's break it down step by step: 1. First, we need to calculate the total score she needs for the entire year to maintain an average of 87. Since there are 8 tests in total, the total score needed is: 87 * 8 = <<87*8=696>>696. 2. Next, let's calculate the total score Nneoma has so far. In the first semester, she had an average of 85, and since there were 4 tests (to make a total of 8 for the year), her total score for the first semester is: 85 * 4 = <<85*4=340>>340. In the second semester, she scored 90, 78, and 92 on her first three tests, so her total score so far in the second semester is: 90 + 78 + 92 = <<90+78+92=260>>260. 3. Now, let's find out how much more she needs to reach the total score of 696. The total score she has so far is 340 (from the first semester) + 260 (from the second semester) = <<340+260=600>>600. So, she needs 696 - 600 = <<696-600=96>>96 more points from her last test to maintain an average of at least 87. Therefore, the minimum score she must get on her last test is 96. #### 96

Mariana and her friends are playing a game of capture the flag in a large park in Rio de Janeiro. The probability of Mariana capturing a flag in a single round is 2/5. If she plays 5 rounds, what is the probability that she captures the flag exactly 3 times?

To solve this, we'll use the binomial probability formula, which is P(X = k) = (nCk) * (p^k) * ((1-p)^(n-k)), where n is the number of trials, k is the number of successful trials, nCk is the number of combinations of n items taken k at a time, p is the probability of success on a single trial, and (1-p) is the probability of failure on a single trial. 1. Define the variables: n = 5 (the number of rounds), k = 3 (the number of times Mariana captures the flag), p = 2/5 (the probability of capturing a flag in a single round). 2. Calculate the probability of failure on a single trial: 1 - p = 1 - 2/5 = 3/5. 3. Calculate the number of combinations for 5 items taken 3 at a time (5C3): 5C3 = 5! / (3! * (5-3)!) = 10. 4. Apply the binomial probability formula: P(X = 3) = 10 * ((2/5)^3) * ((3/5)^2). 5. Calculate each part of the formula: (2/5)^3 = <<(2/5)^3=8/125>>8/125 and (3/5)^2 = <<(3/5)^2=9/25>>9/25. 6. Combine these parts into the formula: P(X = 3) = 10 * (8/125) * (9/25) = <<10*(8/125)*(9/25)=144/625>>144/625. 7. Convert the fraction to a decimal if necessary, but since the question does not specify this, we'll leave the answer as a fraction. Therefore, the probability that Mariana captures the flag exactly 3 times in 5 rounds is 144/625.#### 0.2304

During Hanukkah, the Levi family and their guests consume a total of 48 sufganiyot over the 8-day holiday, with the ratio of guests to family members being 3:5. If the family eats sufganiyot in the same ratio as the number of guests to family members, how many sufganiyot does the family eat?

To solve this problem, we'll follow these steps: 1. First, we need to find the total number of parts in the ratio, which is 3 + 5 = <<3+5=8>>8. 2. Since the total number of sufganiyot is 48 and the total parts are 8, we can find out how many sufganiyot each part represents by dividing the total sufganiyot by the total parts: 48 / 8 = <<48/8=6>>6 sufganiyot per part. 3. The family's portion is represented by 5 parts of the ratio. So, to find out how many sufganiyot the family eats, we multiply the number of parts representing the family by the number of sufganiyot per part: 5 * 6 = <<5*6=30>>30 sufganiyot. Therefore, the family eats 30 sufganiyot during Hanukkah. #### 30

Tomás has been saving money for a new bike and has $120 in his savings account. He wants to buy a bike that costs $180. Tomás' parents have agreed to give him an allowance of $5 per week for doing chores. However, Tomás also spends $2 per week on snacks. How many weeks will it take Tomás to have enough money to buy the bike?

Let's break this down step by step: 1. First, we need to find out how much more money Tomás needs to buy the bike: He needs $180 for the bike and has $120 in savings. So, the amount needed is $180 - $120 = <<180-120=60>>$60. 2. Tomás earns $5 per week from his allowance but spends $2 on snacks. His net savings per week are $5 - $2 = <<5-2=3>>$3. 3. To find out how many weeks it will take to save $60, we divide the amount needed by his weekly savings: $60 / $3 per week = <<60/3=20>>20 weeks. Therefore, it will take Tomás 20 weeks to have enough money to buy the bike. #### 20

During Hanukkah, Rachel and her family traditionally make sufganiyot, Israeli jelly-filled doughnuts. They need to package 3/4 of a kilogram of powdered sugar into bags that hold 1/8 of a kilogram each for a holiday party. How many bags can they fill with the powdered sugar they have?

To find out how many bags can be filled, we need to divide the total amount of powdered sugar by the amount each bag can hold. 1. First, we identify the total amount of powdered sugar and the capacity of each bag: Total powdered sugar = 3/4 kilogram Capacity per bag = 1/8 kilogram 2. To find out how many bags can be filled, we divide the total amount of powdered sugar by the capacity per bag: Number of bags = Total powdered sugar / Capacity per bag 3. Now, we perform the division: Number of bags = (3/4) / (1/8) = (3/4) * (8/1) = 24/4 = <<24/4=6>>6 Therefore, Rachel and her family can fill 6 bags with the powdered sugar they have. #### 6

It's Carnaval time in Rio, and Ana wants to create a costume with a unique blend of colors. She decides to dye a white t-shirt using a combination of blue and yellow dyes. The amount of blue dye needed is given by the polynomial 2x^2 + 5x - 3, where x is the number of yellow dye packets used. If Ana wants to use 4 packets of yellow dye, how many packets of blue dye will she need?

Let's solve this step by step: 1. We need to find the amount of blue dye needed when Ana uses 4 packets of yellow dye. This means we need to substitute x = 4 into the polynomial 2x^2 + 5x - 3. 2. Substitute x = 4 into the polynomial: 2(4)^2 + 5(4) - 3 3. Calculate the exponent first: (4)^2 = <<4^2=16>> 4. Now, substitute this back into the polynomial: 2(16) + 5(4) - 3 5. Multiply 2 by 16: 2(16) = <<2*16=32>> 6. Multiply 5 by 4: 5(4) = <<5*4=20>> 7. Now we have: 32 + 20 - 3 8. Add and subtract from left to right: 32 + 20 = <<32+20=52>> 9. Then subtract 3: 52 - 3 = <<52-3=49>> Therefore, Ana will need 49 packets of blue dye. #### 49

During the annual Copa México soccer tournament, Carlos' team scored 25 goals in the first 5 games. If this represents a 20% increase from last year's average, how many goals did Carlos' team score on average per game last year?

Let's solve this step by step: 1. First, we need to find the total goals scored last year. Let's call this number x. 2. Since there was a 20% increase, the number of goals scored this year is 120% of last year's number, which is the same as 1.2 times last year's number. 3. We know that 1.2 times last year's number equals 25 goals. So, we can set up the equation 1.2x = 25. 4. To find x, we need to divide both sides of the equation by 1.2: x = 25 / 1.2 = <<25/1.2=20.83>>. 5. Since this is the total for 5 games, we need to find the average goals scored per game last year. To do this, we divide the total goals by the number of games: 20.83 / 5 = <<20.83/5=4.17>>. 6. Therefore, the average goals scored per game last year was 4.17. 7. Rounding is not needed as we are asked for an exact average based on the given data. #### 4.17

Yuna is making a traditional Japanese dessert called "Mochi" for the New Year's celebration. The recipe requires a ratio of 2 cups of glutinous rice flour to 1 cup of granulated sugar. If Yuna wants to make 3 batches of Mochi and each batch requires 1.5 cups of sugar, how many cups of glutinous rice flour will she need in total?

Let's solve this step by step: 1. First, determine the amount of sugar needed for 3 batches: 3 batches * 1.5 cups/batch = <<3*1.5=4.5>>4.5 cups 2. Since the ratio of glutinous rice flour to sugar is 2:1, we can find the amount of glutinous rice flour needed by multiplying the amount of sugar by 2: 4.5 cups * 2 = <<4.5*2=9>>9 cups Therefore, Yuna will need 9 cups of glutinous rice flour in total. #### 9

Hans is traveling from Berlin to Munich, a distance of 340 miles. If he drives for 2/5 of the distance in the morning and then stops for lunch, how many miles does he still have to drive in the afternoon to reach Munich?

Let's break this down step by step: 1. First, we need to find out how far Hans drove in the morning. To do this, we'll multiply the total distance by the fraction of the distance he covered in the morning: 340 miles * 2/5 = <<340 * 2 / 5 = 136>>136 miles. 2. Now, we need to find out how many miles Hans still has to drive in the afternoon. We'll subtract the distance covered in the morning from the total distance: 340 miles - 136 miles = <<340 - 136 = 204>>204 miles. Therefore, Hans still has to drive 204 miles in the afternoon to reach Munich. #### 204

Pierre is baking a large batch of croissants for a French bakery. He needs to package 480 croissants into boxes that hold 12 each. How many boxes can Pierre fill with the croissants he has baked?

Let's solve this step by step: 1. First, we need to determine how many boxes Pierre can fill with 480 croissants if each box holds 12 croissants. 2. To find this, we divide the total number of croissants by the number of croissants each box can hold: 480 ÷ 12 = <<480/12=40>> Therefore, Pierre can fill 40 boxes with the croissants he has baked. #### 40

At a Thai festival, Nong and her friends want to share some candies equally. If they have 480 candies to share and there are 8 friends, but 3 more friends join in, how many candies will each friend get now?

Let's solve this step by step: 1. Initially, there are 8 friends sharing 480 candies. 2. To find out how many candies each friend would get before the 3 extra friends join, we divide the total candies by the number of friends: <<480 / 8 = 60>> candies per friend. 3. However, 3 more friends join, changing the total number of friends: 8 original friends + 3 new friends = <<8 + 3 = 11>> friends now. 4. We need to recalculate the number of candies each friend will get with the new total number of friends: Total candies / new total number of friends = <<480 / 11 = 43.63636363636363>> candies per friend. 5. Since candies cannot be divided into fractions, we round down to the nearest whole number to ensure each friend gets an equal and whole number of candies: 43.63636363636363 → 43 candies per friend (after rounding down). 6. To verify our solution, we can check if we have enough candies for each friend to get 43 candies: Total candies needed = 43 candies/friend * 11 friends = <<43 * 11 = 473>> candies. 7. We see that we have enough candies (480) for each of the 11 friends to get 43 candies, with some candies left over. 8. Therefore, each friend will get 43 candies. #### 43

At a Canada Day celebration in Ottawa, 3 large bags of popcorn are needed to serve 18 people. If 72 people are expected to attend the event, how many large bags of popcorn should be prepared?

Let's solve this step by step: 1. First, determine the number of people one large bag of popcorn can serve: 18 people / 3 bags = <<18/3=6>>6 people per bag 2. Calculate how many bags are needed for 72 people: 72 people / 6 people per bag = <<72/6=12>>12 bags Therefore, 12 large bags of popcorn should be prepared. #### 12

Fatima is traveling from Dubai to Cairo, a distance of 2,150 kilometers. If she travels 3/5 of the distance by plane and the rest by car, and the plane travels at an average speed of 600 km/h, how many hours will she spend on the plane?

To find out how many hours Fatima will spend on the plane, we first need to calculate the distance she travels by plane. The total distance is 2,150 kilometers, and she travels 3/5 of this distance by plane. 1. First, calculate 3/5 of 2,150 kilometers: 3/5 * 2,150 = <<3/5 * 2150 = 1290>> kilometers. 2. Now that we know the distance traveled by plane is 1,290 kilometers, and the plane travels at an average speed of 600 km/h, we can calculate the time spent on the plane using the formula time = distance / speed. 3. Calculate the time spent on the plane: time = 1,290 kilometers / 600 km/h = <<1290 / 600 = 2.15>> hours. Therefore, Fatima will spend 2.15 hours on the plane. #### 2.15

Tom, a young birdwatcher from Munich, observed that a flock of migratory birds was traveling at an average speed of 25 km/h. If the birds flew for 4 hours in the morning and then rested for 2 hours before resuming their flight for another 3 hours in the evening, how many kilometers did they cover in total?

Let's break this down step by step: 1. First, calculate the distance covered by the birds in the morning: Speed = 25 km/h, Time = 4 hours Distance = Speed * Time = <<25 * 4 = 100>> km 2. The birds rested for 2 hours, so no distance was covered during this time. 3. Then, calculate the distance covered by the birds in the evening: Speed = 25 km/h, Time = 3 hours Distance = Speed * Time = <<25 * 3 = 75>> km 4. Finally, add the distances covered in the morning and evening to find the total distance: Total Distance = 100 km + 75 km = <<100 + 75 = 175>> km Therefore, the birds covered a total distance of 175 kilometers. #### 175

It's Cinco de Mayo, and Maria's family is preparing for their annual celebration. They've ordered a piñata that's on sale for 15% off its original price of $25. How much will Maria's family pay for the piñata?

Let's break this down step by step: 1. First, we need to find the discount amount by calculating 15% of the original price of $25. Discount = 15% of $25 = <<15/100 * 25 = 3.75>>$ 2. Next, we subtract the discount from the original price to find the sale price. Sale price = Original price - Discount = $25 - $3.75 = <<25 - 3.75 = 21.25>>$ 3. Therefore, Maria's family will pay the sale price for the piñata. 4. The final amount Maria's family will pay is the sale price. #### 21.25

Tomás is planning a family reunion in Rio de Janeiro and needs to buy food for 25 people, including his large Brazilian family and some American relatives. He wants to serve feijoada, which costs 50 reais per kilogram. If he needs at least 0.5 kilograms of feijoada per person and has a 15% discount coupon for purchases over 1000 reais, how much will Tomás pay in total for the feijoada?

Let's break down the problem step by step: 1. First, calculate the total amount of feijoada needed for 25 people: 25 people * 0.5 kilograms/person = <<25 * 0.5 = 12.5>> kilograms 2. Now, calculate the total cost before the discount: 12.5 kilograms * 50 reais/kilogram = <<12.5 * 50 = 625>> reais 3. Check if the purchase is eligible for the discount: Since 625 reais is less than 1000 reais, the discount does not apply directly. 4. However, we should consider that the problem might be testing our understanding of the discount condition: Given the initial calculation, there seems to be a misunderstanding in interpreting the discount application criteria. 5. Realizing the mistake, let's correct our approach: The actual total needed is indeed 12.5 kilograms, and the cost before discount is correctly calculated as 625 reais. 6. Since the total cost is below the discount threshold, Tomás will pay the full amount without any discount. 7. Therefore, no additional calculations are required regarding the discount. 8. The total amount Tomás will pay for the feijoada remains the initial calculated cost. #### 625

Mei-Ling is traveling from Beijing to Shanghai, a distance of 1,200 kilometers. If she takes a high-speed train that travels at an average speed of 300 kilometers per hour, and the train makes a 30-minute stop at a station along the way, how many hours will Mei-Ling spend on the train in total?

To solve this problem, let's break it down into steps: 1. Calculate the total travel time without the stop: Total distance / Speed = <<1200 / 300 = 4>> hours. 2. Convert the 30-minute stop to hours: 30 minutes / 60 minutes per hour = <<30 / 60 = 0.5>> hours. 3. Add the stop time to the travel time to get the total time spent on the train: Total travel time + Stop time = 4 hours + 0.5 hours = <<4 + 0.5 = 4.5>> hours. Therefore, Mei-Ling will spend 4.5 hours on the train in total. #### 4.5

Pierre is building a scale model of the Eiffel Tower using wood and needs to calculate the total length of wood required for the project. The model's design requires 3/4 of a meter for the base, 1/2 meter for the middle section, and 1/6 meter for the top. If Pierre has a 2-meter long piece of wood, how many centimeters of wood will he have left after completing the model?

Let's break down the problem step by step: 1. First, we need to calculate the total length of wood required for the project. We have three sections: base, middle, and top, with lengths 3/4 meter, 1/2 meter, and 1/6 meter respectively. 2. To add these fractions, we need a common denominator, which is 12. So we convert each fraction: 3/4 = 9/12, 1/2 = 6/12, and 1/6 = 2/12. 3. Now, we add the fractions: 9/12 + 6/12 + 2/12 = 17/12 meters. To convert this to a mixed number, we divide 17 by 12, which gives 1 with a remainder of 5, so 17/12 = 1 5/12 meters. 4. Since Pierre has a 2-meter long piece of wood, we subtract the required length from it to find out how much wood he'll have left: 2 - 1 5/12. To perform this subtraction, we convert 2 to a mixed number with the same denominator: 2 = 2 0/12. Then we subtract: 2 0/12 - 1 5/12 = 0 7/12 meters. 5. Finally, to convert the remaining length from meters to centimeters (since 1 meter = 100 centimeters), we multiply 0 7/12 meters by 100: 7/12 * 100 = <<7/12*100=58.33>>58.33 centimeters. Therefore, Pierre will have 58.33 centimeters of wood left after completing the model. #### 58.33

Min-ju is having a picnic in the park and wants to buy a new frisbee that is on sale for 15% off its original price of ₩25,000. How much will Min-ju pay for the frisbee?

To find the price Min-ju will pay, let's first calculate the discount amount and then subtract it from the original price. 1. Calculate the discount amount: 15% of 25,000 = <<15/100 * 25000 = 3750>> 2. Subtract the discount from the original price to find the sale price: 25,000 - 3750 = <<25000 - 3750 = 21250>> Therefore, Min-ju will pay 21,250 for the frisbee. #### 21250

During Carnaval in Rio de Janeiro, a street vendor sells decorative paper flowers in the shape of spheres. If each flower has a diameter of 20 cm, what is the volume of a single flower in cubic centimeters?

To find the volume of the decorative paper flower, which is in the shape of a sphere, we use the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius of the sphere. 1. Given the diameter of the flower is 20 cm, we first find the radius: Radius (r) = diameter / 2 = 20 / 2 = <<20/2=10>>10 cm 2. Now, we apply the formula for the volume of a sphere: V = (4/3)πr^3 3. Substitute the value of r into the formula: V = (4/3)π(10)^3 4. Calculate the volume step by step: V = (4/3) * π * 1000 V = (4/3) * 3.14159 * 1000 V = <<(4/3)*3.14159*1000=4188.79>>4188.79 cubic cm Therefore, the volume of a single flower is approximately 4188.79 cubic centimeters. #### 4189

Yael is shopping during a holiday sale in Tel Aviv. She finds a shirt originally priced at 250 ILS. The store is offering a 15% discount on all items. How much will Yael pay for the shirt after the discount?

To find the amount Yael will pay, we need to calculate the discount first and then subtract it from the original price. 1. The original price of the shirt is 250 ILS. 2. The discount offered is 15% of the original price: 15% of 250 = <<15/100 * 250 = 37.5>>ILS 3. To find the price after the discount, subtract the discount from the original price: Price after discount = Original price - Discount = 250 - 37.5 = <<250 - 37.5 = 212.5>>ILS Therefore, Yael will pay 212.5 ILS for the shirt after the discount. #### 212.5