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A recipe for making jollof rice for the Uwagboe family reunion requires a ratio of 2 cups of rice to 3 cups of water. If Mrs. Uwagboe wants to cook 6 cups of rice, how many cups of water will she need?

To solve this problem, we need to use the ratio of rice to water given in the recipe to find the amount of water needed for 6 cups of rice. Step 1: First, we need to identify the parts of the ratio. The ratio of rice to water is 2:3, which means for every 2 cups of rice, we need 3 cups of water. Step 2: We want to cook 6 cups of rice, so we need to find out how many sets of 2 cups of rice we have. To do this, we divide 6 by 2: <<6/2=3>> This means we have 3 sets of 2 cups of rice. Step 3: Since we have 3 sets of 2 cups of rice, and the ratio of rice to water is 2:3, we need 3 sets of 3 cups of water. To find the total amount of water needed, we multiply 3 (the number of sets) by 3 (the amount of water per set): <<3*3=9>> Therefore, Mrs. Uwagboe will need 9 cups of water to cook 6 cups of rice. #### 9

Rohan is making a traditional Indian dessert called Gulab Jamun for a family gathering. The recipe calls for 2 cups of milk powder to make 20 pieces. If Rohan wants to make 30 pieces, how many cups of milk powder should he use?

Let's solve this step by step: 1. First, determine the amount of milk powder needed per piece of Gulab Jamun in the original recipe: 2 cups of milk powder / 20 pieces = <<2/20=0.1>>0.1 cups per piece 2. To make 30 pieces, multiply the amount of milk powder needed per piece by the number of pieces Rohan wants to make: 0.1 cups per piece * 30 pieces = <<0.1*30=3>>3 cups Therefore, Rohan should use 3 cups of milk powder to make 30 pieces of Gulab Jamun. #### 3

Çağatay is the manager of a Turkish basketball team. He needs to buy new basketballs for the upcoming season. The team has a budget of ₺500 for the balls. Each high-quality ball costs ₺25, and each regular ball costs ₺15. If Çağatay wants to buy at least 20 balls in total and ensure that at least 40% of the balls are high-quality, how many of each type of ball should he purchase to maximize the number of balls within the budget?

Let's solve this step by step: 1. Define variables: Let x be the number of high-quality balls, and y be the number of regular balls. 2. Set up the objective function to maximize the total number of balls: Total balls = x + y 3. Constraints: Budget constraint: 25x + 15y ≤ 500 Total balls constraint: x + y ≥ 20 High-quality balls constraint: x ≥ 0.4(x + y) Non-negativity: x ≥ 0, y ≥ 0 4. Solve for x in terms of y from the high-quality balls constraint: x ≥ 0.4x + 0.4y 0.6x ≥ 0.4y x ≥ (2/3)y 5. Substitute x in the budget constraint: 25((2/3)y) + 15y ≤ 500 (50/3)y + 15y ≤ 500 (50y + 45y)/3 ≤ 500 95y ≤ 1500 y ≤ 1500/95 y ≤ 15.79 Since y must be an integer, the maximum y is 15. 6. Find the corresponding x when y = 15: x ≥ (2/3)*15 x ≥ 10 Checking the budget for x = 10 and y = 15: 25*10 + 15*15 = 250 + 225 = <<250+225=475>>475 Since this is within the budget, we can purchase 10 high-quality balls and 15 regular balls. Therefore, Çağatay should buy 10 high-quality balls and 15 regular balls to maximize the number of balls within the budget. #### 25

Luana invests R$1,500 in a craft store to buy materials for her jewelry-making hobby. The money earns an annual interest rate of 6%, compounded semiannually. How much money will Luana have after 2 years to spend on new beads and threads?

Let's break this down step by step: 1. First, we need to calculate the number of compounding periods. Since the interest is compounded semiannually, there will be 2 compounding periods per year. For 2 years, the total number of compounding periods is 2 * 2 = <<2*2=4>>4 periods. 2. Next, we calculate the interest rate per compounding period. The annual interest rate is 6%, so the rate per compounding period is 6% / 2 = 3% = 0.03. 3. Now, we apply the compound interest formula: A = P * (1 + r)^n, where A is the amount after n periods, P is the principal amount (initial investment), r is the interest rate per period, and n is the number of periods. Plugging in the values, we get: A = 1500 * (1 + 0.03)^4 = 1500 * (1.03)^4. Calculating this: (1.03)^4 = <<1.03^4=1.125984>>1.125984. So, A = 1500 * 1.125984 = <<1500*1.125984=1688.976>>1688.976. Therefore, Luana will have approximately R$1688.98 after 2 years to spend on new beads and threads. #### 1688.98

Léa observes that her cat, Félix, eats 1/4 of a bag of cat food every week. If she buys a new bag that contains 3/4 of the usual amount, how many weeks will it last Félix?

Let's solve this step by step: 1. First, we need to understand that if F\u00e9lix eats 1/4 of a bag every week, a full bag would last 4 weeks because 1 divided by 1/4 equals 4 <<1 / (1/4) = 4>>. 2. Since L\u00e9a buys a bag that contains 3/4 of the usual amount, we need to find out how long this reduced amount will last. 3. Knowing that the full bag lasts 4 weeks, we can calculate the duration of the 3/4 bag by multiplying the full bag's duration by 3/4: 4 * 3/4 = 3 <<4 * 3/4 = 3>>. Therefore, the new bag of cat food will last F\u00e9lix 3 weeks. #### 3

Nguyễn Thị Mai has been tracking the number of books read by her class over the past few months. In the first month, they read 15 books. In the second month, they read 24 books. If the ratio of books read in the first month to the second month is 5:8, how many books should they read in the third month to maintain a ratio of 5:8:12 for the three months?

Let's solve this step by step: 1. First, let's determine the total number of parts in the ratio: 5 + 8 + 12 = <<5+8+12=25>>25 parts. 2. Since we know the number of books read in the first two months, we can find the value of one part of the ratio by dividing the number of books read by the corresponding number of parts in the ratio. We'll use the number of books from the first month: 15 books / 5 parts = <<15/5=3>>3 books per part. 3. Now, we can verify if the number of books read in the second month aligns with this value: 24 books / 8 parts = <<24/8=3>>3 books per part, which matches our calculation. 4. To maintain the ratio, we need to find out how many books should be read in the third month, which corresponds to 12 parts of the ratio. Since one part equals 3 books, the number of books for 12 parts is: 3 books/part * 12 parts = <<3*12=36>>36 books. 5. Therefore, the class needs to read 36 books in the third month to maintain the ratio of 5:8:12 for the three months. 6. By following this approach, we ensure that the ratio of books read in the three months remains consistent. #### 36

Sergei is planning a road trip from Moscow to St. Petersburg, which is approximately 700 kilometers away. His car's fuel tank can hold 50 liters of gasoline. If his car consumes an average of 10 kilometers per liter of gasoline, and gasoline costs 45 rubles per liter, how many rubles will Sergei spend on gasoline for the entire trip, assuming he starts with a full tank and does not refill until he reaches St. Petersburg?

To solve this, let's break it down into steps: 1. First, we need to determine how many liters of gasoline Sergei's car will consume for the entire trip. We can do this by dividing the total distance by the car's fuel efficiency (kilometers per liter). Total distance = 700 kilometers Fuel efficiency = 10 kilometers/liter Total fuel consumption = Total distance / Fuel efficiency = <<700 / 10 = 70>> liters 2. However, Sergei's car can only hold 50 liters of gasoline. Since he won't refill until he reaches St. Petersburg, we only need to consider the fuel his tank can hold for the calculation of cost, as he cannot use more than this amount for the trip. Therefore, we use the tank's capacity for calculating the cost. Fuel to be used for cost calculation = 50 liters 3. Now, we calculate the cost of the gasoline for the trip by multiplying the amount of fuel used by the cost per liter. Cost per liter = 45 rubles Total cost = Fuel to be used for cost calculation * Cost per liter = <<50 * 45 = 2250>> rubles Therefore, Sergei will spend 2250 rubles on gasoline for the entire trip. #### 2250

Kofi and Ama are planning a camping trip in the Ghanaian wilderness. They want to share some snacks, and Kofi has 3/4 of a bag of groundnuts, while Ama has 2/3 of a bag of plantain chips. If they want to combine their snacks into bags that are 1/6 full, how many bags can they fill in total?

Let's solve this step by step: 1. First, we need to find the total amount of snacks they have. To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we convert both fractions to have a denominator of 12: Kofi has 3/4 = 9/12 of a bag of groundnuts. Ama has 2/3 = 8/12 of a bag of plantain chips. 2. Now, we can add the fractions together: Total snacks = 9/12 + 8/12 = <<9+8=17>>17/12 3. They want to fill bags that are 1/6 full. To find out how many bags they can fill, we need to divide the total amount of snacks by 1/6. To divide by a fraction, we can multiply by its reciprocal (i.e., 6): Number of bags = Total snacks * 6 = 17/12 * 6 = <<17*6/12=8.5>>8.5 Since we can't have half a bag, we'll round down to 8 bags, as the bags must be 1/6 full as a minimum requirement. Therefore, Kofi and Ama can fill 8 bags with their snacks. #### 8

At a French wildlife sanctuary, the ratio of birds to rabbits is 5:3. If the total number of birds and rabbits is 72, how many more birds are there than rabbits?

Let's break down the problem step by step: 1. The ratio of birds to rabbits is given as 5:3. This means that for every 5 birds, there are 3 rabbits. 2. The total number of birds and rabbits is 72. We can represent the total number of birds as 5x and the total number of rabbits as 3x, where x is a common multiplier. 3. We can set up an equation to represent the total number of birds and rabbits: 5x + 3x = 72 Combine like terms: 8x = 72 Solve for x: x = <<72 / 8 = 9>> 4. Now that we know x, we can find the number of birds and rabbits: Number of birds = 5x = 5 * 9 = <<5 * 9 = 45>> Number of rabbits = 3x = 3 * 9 = <<3 * 9 = 27>> 5. To find the difference between the number of birds and rabbits, subtract the number of rabbits from the number of birds: Difference = Number of birds - Number of rabbits = 45 - 27 = <<45 - 27 = 18>> Therefore, there are 18 more birds than rabbits. #### 18

Maria is preparing empanadas for a family gathering and needs to package them for the guests. She has 18 empanadas already made and wants to put 3 empanadas in each package. How many more empanadas does Maria need to make so that she can create 8 packages with 3 empanadas in each package?

Let's solve this step by step: 1. First, calculate the total number of empanadas needed for 8 packages with 3 empanadas each: Total empanadas needed = 8 packages * 3 empanadas per package = <<8 * 3 = 24>>empanadas. 2. Then, subtract the number of empanadas Maria already has from the total needed to find out how many more she needs to make: More empanadas needed = Total empanadas needed - Empanadas already made = 24 - 18 = <<24 - 18 = 6>>empanadas. Therefore, Maria needs to make 6 more empanadas. #### 6

During the Cherry Blossom Festival in Tokyo, a traditional Japanese sweets shop sells two types of sakura mochi, A and B. Type A is sold in packs of 5 for ¥2000, and Type B is sold in packs of 3 for ¥1500. If Sara wants to buy exactly 30 pieces of sakura mochi for her family gathering, and she prefers the ratio of Type A to Type B to be 2:3, how much will she spend in total?

To find the total cost, we first need to determine how many packs of each type Sara should buy to achieve the desired ratio and total quantity of 30 pieces. 1. Since the ratio of Type A to Type B should be 2:3, let's calculate the total parts in the ratio: 2 + 3 = <<2+3=5>>5 parts 2. Now, we need to find out how many pieces each part represents by dividing the total quantity by the total parts: 30 / 5 = <<30/5=6>>6 pieces per part 3. Since Type A represents 2 parts, Sara should buy 2 * 6 = <<2*6=12>>12 pieces of Type A 4. And since Type B represents 3 parts, Sara should buy 3 * 6 = <<3*6=18>>18 pieces of Type B 5. Now, let's calculate the number of packs for each type: For Type A, 12 pieces / 5 pieces per pack = <<12/5=2.4>>2.4 packs. Since we can't buy a fraction of a pack, Sara will need to buy 3 packs of Type A (the smallest whole number of packs that provides at least 12 pieces). For Type B, 18 pieces / 3 pieces per pack = <<18/3=6>>6 packs 6. Finally, let's calculate the total cost: 3 packs of Type A * \u00a52000 per pack = <<3*2000=6000>>\u00a56000, and 6 packs of Type B * \u00a51500 per pack = <<6*1500=9000>>\u00a59000. The total cost is \u00a56000 + \u00a59000 = <<6000+9000=15000>>\u00a515000 #### 15000

Ivan is the coach of a junior hockey team in Moscow. The team's current fan base is 250 people, and it has been growing at a rate of 15% every month. If the growth rate remains constant, how many fans will the team have in 6 months?

Let's solve this step by step: 1. First, we need to understand the growth rate. A 15% monthly growth rate means that each month, the fan base will be 115% of the previous month's fan base. 2. To find the number of fans after 6 months, we'll start with the initial number of fans and apply the growth rate 6 times. 3. Initial number of fans = 250 4. After the 1st month: 250 * 1.15 = <<250 * 1.15 = 287.5>>287.5 fans 5. After the 2nd month: 287.5 * 1.15 = <<287.5 * 1.15 = 330.625>>330.625 fans 6. After the 3rd month: 330.625 * 1.15 = <<330.625 * 1.15 = 380.21875>>380.21875 fans 7. After the 4th month: 380.21875 * 1.15 = <<380.21875 * 1.15 = 437.2515625>>437.2515625 fans 8. After the 5th month: 437.2515625 * 1.15 = <<437.2515625 * 1.15 = 502.839453125>>502.839453125 fans 9. After the 6th month: 502.839453125 * 1.15 = <<502.839453125 * 1.15 = 578.2658703125>>578.2658703125 fans Therefore, the team will have approximately 578 fans in 6 months. #### 578

The Chiang Mai Cricket Club has been growing its membership at an annual rate of 15%. If the club currently has 120 members, how many members will it have in two years?

Let's solve this step by step: 1. First, we need to find the number of members after one year. To do this, we'll calculate 15% of the current number of members and add it to the current number. The current number of members is 120. 15% of 120 = <<120 * 15 / 100 = 18>> members. So, after one year, the club will have 120 + 18 = <<120 + 18 = 138>> members. 2. Now, we'll repeat the process for the second year, using the number of members after one year as the base. 15% of 138 = <<138 * 15 / 100 = 20.7>> members. So, after two years, the club will have 138 + 20.7 = <<138 + 20.7 = 158.7>> members. Since we can't have a fraction of a member, we'll round to the nearest whole number: 159 members. Therefore, the Chiang Mai Cricket Club will have 159 members in two years. #### 159

Madame Dupont is planning a school trip to the Eiffel Tower for her class of 30 students. The bus rental company charges a flat fee of 150 euros plus an additional 5 euros per student. If the total cost of the bus rental is to be split equally among the students, and Madame Dupont has a 15% discount coupon for the total cost, how much will each student need to pay?

Let's break this down step by step: 1. First, calculate the total cost of the bus rental before the discount: The flat fee is 150 euros, and there's an additional 5 euros per student. With 30 students: Total cost = flat fee + (additional cost per student * number of students) = 150 + (5 * 30) = 150 + <<5 * 30 = 150>>150 = <<150 + 150 = 300>>300 euros 2. Next, apply the 15% discount to the total cost: Discount amount = 15% of 300 euros = 0.15 * 300 = <<0.15 * 300 = 45>>45 euros 3. Subtract the discount from the total cost to find the final cost after the discount: Final cost = total cost - discount amount = 300 - 45 = <<300 - 45 = 255>>255 euros 4. Since the cost is to be split equally among the students, divide the final cost by the number of students: Cost per student = final cost / number of students = 255 / 30 = <<255 / 30 = 8.5>>8.5 euros Therefore, each student needs to pay 8.5 euros. #### 8.5

The Rodriguez family is decorating their house for Christmas. They want to put a string of lights around the perimeter of their rectangular front yard, which measures 25 feet by 30 feet. If they have a 100-foot string of lights, how many feet of lights will they have left over after decorating the yard?

To find out how many feet of lights the Rodriguez family will have left over after decorating their yard, we need to calculate the perimeter of the rectangular front yard and subtract this from the total length of the string of lights. 1. First, let's calculate the perimeter of the rectangular yard: The formula for the perimeter of a rectangle is P = 2(length + width). Given the length (L) is 30 feet and the width (W) is 25 feet, we can substitute these values into the formula: P = 2(30 + 25) = 2 * <<30 + 25 = 55>>55 = <<2 * 55 = 110>>110 feet. 2. Since they have a 100-foot string of lights, which is less than the perimeter of the yard, they won't have enough lights to go around the entire yard. However, the question asks how many feet of lights they will have left over, implying we should still calculate the difference for clarity, though the correct interpretation leads to understanding they won't have enough. The misunderstanding in the initial calculation aim is clarified by recognizing the need to simply state they won't have enough based on the given dimensions and string length. Thus, the actual step needed is acknowledging the error in assuming they'd have leftover lights given the initial setup. Given the string of lights is 100 feet and the perimeter is 110 feet, they won't have enough lights to encircle the yard, but to directly answer the original question's intent without further misinterpretation: the calculation aimed to find leftover length would show they're short, not having extra. Therefore, correcting for the context provided and clarifying the error in logic applied: #### 0

Anastasia is planning a trip from Moscow to St. Petersburg. The distance between the two cities is approximately 700 kilometers. If she takes a high-speed train traveling at an average speed of 200 kilometers per hour, but then boards a local train that travels at 50 kilometers per hour for the last 100 kilometers, how many hours will her total journey take?

Let's solve this step by step: 1. First, calculate the distance covered by the high-speed train: Total distance = 700 km Distance covered by local train = 100 km Distance covered by high-speed train = Total distance - Distance covered by local train = 700 km - 100 km = <<700 - 100 = 600>>600 km 2. Calculate the time taken by the high-speed train: Speed of high-speed train = 200 km/h Time taken = Distance / Speed = 600 km / 200 km/h = <<600 / 200 = 3>>3 hours 3. Calculate the time taken by the local train: Speed of local train = 50 km/h Time taken = Distance / Speed = 100 km / 50 km/h = <<100 / 50 = 2>>2 hours 4. Find the total time taken for the journey: Total time = Time taken by high-speed train + Time taken by local train = 3 hours + 2 hours = <<3 + 2 = 5>>5 hours Therefore, Anastasia's total journey will take 5 hours. #### 5

Sasha and her family are planning a trip to Moscow. They have a budget of 15,000 rubles for accommodations. If they spend 2,500 rubles per night, how many nights can they afford to stay in Moscow?

Let's break this down step by step: 1. First, we need to identify the total budget for accommodations, which is given as 15,000 rubles. 2. Next, we know the cost per night is 2,500 rubles. 3. To find out how many nights they can afford, we'll divide the total budget by the cost per night: <<15000 / 2500 = 6>> Therefore, Sasha and her family can afford to stay in Moscow for 6 nights. #### 6

Kuzma has 15 boxes of pryaniki to sell at the Moscow market, with 24 pryaniki in each box. He wants to package them in bags of 6 for individual sale. How many bags can Kuzma make with the pryaniki he has?

Let's solve this step by step: 1. First, we need to find out how many pryaniki Kuzma has in total. Since he has 15 boxes with 24 pryaniki in each box, we multiply the number of boxes by the number of pryaniki in each box: Total pryaniki = 15 boxes * 24 pryaniki/box = <<15*24=360>>360 pryaniki 2. Now, we need to determine how many bags Kuzma can make with the total number of pryaniki he has. Since each bag will contain 6 pryaniki, we divide the total number of pryaniki by the number of pryaniki per bag: Total bags = Total pryaniki / pryaniki per bag = 360 pryaniki / 6 pryaniki/bag = <<360/6=60>>60 bags Therefore, Kuzma can make 60 bags with the pryaniki he has. #### 60

Lan Nguyen has been observing the growth of a bamboo plant in her backyard. If the plant grows 3/5 of a meter in the first week and 2/3 of a meter in the second week, how many meters will it have grown in total after two weeks?

Let's break this down step by step: 1. First, let's find a common denominator for the fractions 3/5 and 2/3. The least common multiple of 5 and 3 is 15. 2. Convert both fractions to have a denominator of 15: 3/5 = 9/15 and 2/3 = 10/15. 3. Now, add the fractions together: 9/15 + 10/15 = <<9 + 10 = 19>>19/15. 4. Since 19 is greater than 15, we can convert this improper fraction to a mixed number: 1 4/15. 5. Therefore, the bamboo plant will have grown 1 and 4/15 meters in total after two weeks. 6. To find the decimal equivalent, we can divide the numerator of the fraction by the denominator and add it to the whole number part: 1 + 4/15 = 1 + <<4 / 15 = 0.2667>>0.2667 = 1.2667 meters. #### 1.2667

Ngọc invested 1,000,000 Vietnamese đồng in a savings account that earns a 5% annual interest rate compounded annually. If she doesn't make any withdrawals, how much money will she have in her account after 2 years?

Let's break this down step by step: 1. First, we need to calculate the interest earned in the first year: Interest for the first year = Principal * Rate = 1,000,000 * 5% = <<1000000 * 5 / 100 = 50000>>50,000 Vietnamese đồng 2. The total amount after the first year = Principal + Interest = 1,000,000 + 50,000 = <<1000000 + 50000 = 1050000>>1,050,000 Vietnamese đồng 3. Now, we calculate the interest for the second year using the new principal (total amount after the first year): Interest for the second year = New Principal * Rate = 1,050,000 * 5% = <<1050000 * 5 / 100 = 52500>>52,500 Vietnamese đồng 4. Finally, the total amount after 2 years = New Principal + Interest = 1,050,000 + 52,500 = <<1050000 + 52500 = 1102500>>1,102,500 Vietnamese đồng Therefore, after 2 years, Ngọc will have 1,102,500 Vietnamese đồng in her account. #### 1102500

Lena ist eine deutsche Künstlerin, die eine maßstabsgetreue Skulptur des Berliner Fernsehturms erstellt. Wenn das Original 368 Meter hoch ist und Lena ihre Skulptur auf 1:1000 verkleinert, wie viele Zentimeter hoch sollte ihre Skulptur sein, wenn 1 Meter 100 Zentimetern entspricht?

Lassen Sie uns das Schritt für Schritt lösen: 1. Zuerst müssen wir die Höhe der Skulptur in Metern ermitteln. Da das Original 368 Meter hoch ist und Lena ihre Skulptur auf 1:1000 verkleinert, müssen wir 368 Meter durch 1000 teilen, um die Höhe der Skulptur in Metern zu erhalten: <<368/1000=0.368>> Meter. 2. Da 1 Meter 100 Zentimetern entspricht, können wir die Höhe der Skulptur in Zentimeter umrechnen, indem wir die Höhe in Metern mit 100 multiplizieren: <<0.368*100=36.8>> Zentimeter. Daher sollte Lenas Skulptur 36,8 Zentimeter hoch sein. #### 36.8

Hans is building a treehouse and needs to maximize the area of the rectangular floor given a fixed perimeter of 24 meters. The length of the floor must be 2 meters more than the width. What is the maximum area Hans can achieve for the floor?

Let's solve this step by step: 1. Define the variables: Let w be the width of the floor, and l be the length of the floor. We are given that l = w + 2. 2. The perimeter P of a rectangle is given by the formula P = 2l + 2w. We are given that the perimeter is 24 meters, so we can set up the equation 24 = 2l + 2w. 3. Substitute l = w + 2 into the equation: 24 = 2(w + 2) + 2w. 4. Expand the equation: 24 = 2w + 4 + 2w. 5. Combine like terms: 24 = 4w + 4. 6. Subtract 4 from both sides: 20 = 4w. 7. Divide both sides by 4: 5 = w. 8. Now that we have the width, we can find the length: l = w + 2 = 5 + 2 = 7. 9. The area A of a rectangle is given by the formula A = l * w. We can now calculate the maximum area: A = 7 * 5 = <<7*5=35>>. Therefore, the maximum area Hans can achieve for the floor is 35 square meters. #### 35

Yuna is planning her sister's birthday party in Tokyo and wants to buy a gift within her budget of ¥25,000. She finds a beautiful kimono that is on sale for 15% off its original price of ¥30,000. However, there's an additional 5% discount for students, which Yuna is eligible for. How much will Yuna pay for the kimono after both discounts are applied?

To find the final price Yuna will pay, we'll apply the discounts step by step. 1. First, calculate the price after the initial 15% discount: The discount amount is 15% of \u00a530,000: 15% of \u00a530,000 = <<15/100 * 30000 = 4500>>\u00a54,500 So, the price after the first discount is: \u00a530,000 - \u00a54,500 = <<30000 - 4500 = 25500>>\u00a525,500 2. Next, apply the additional 5% student discount on the already discounted price of \u00a525,500: 5% of \u00a525,500 = <<5/100 * 25500 = 1275>>\u00a51,275 Therefore, the final price after both discounts is: \u00a525,500 - \u00a51,275 = <<25500 - 1275 = 24225>>\u00a524,225 #### 24225

Tomás is planning a camping trip with his friends in the mountains of Chihuahua. He wants to make sure they have enough snacks for the 5-day trip. If they need 3 bags of trail mix for every 2 days of camping, and each bag contains 2.5 kilograms of mix, how many kilograms of trail mix should Tomás buy for the entire trip?

To find out how many kilograms of trail mix Tom\u00e1s should buy, we need to follow these steps: 1. Determine how many bags of trail mix are needed for the 5-day trip: Since they need 3 bags of trail mix for every 2 days of camping, for 5 days, we calculate the number of sets of 2 days: 5 days / 2 days per set = <<5/2=2.5>>2.5 sets Since we can't have half a set in practical terms, we'll consider the whole number part (2 sets) and then account for the remaining days separately. 2 sets * 3 bags per set = <<2*3=6>>6 bags for the first 4 days For the remaining 1 day, if 3 bags are needed for 2 days, for 1 day we would need half of that amount: 3 bags / 2 days * 1 day = <<3/2*1=1.5>>1.5 bags Adding this to the bags for the first 4 days: 6 bags + 1.5 bags = <<6+1.5=7.5>>7.5 bags Since we can't buy half a bag, we round up to the nearest whole number for practical purposes, resulting in 8 bags needed. 2. Calculate the total kilograms of trail mix needed: Each bag contains 2.5 kilograms of mix, so for 8 bags: 8 bags * 2.5 kilograms per bag = <<8*2.5=20>>20 kilograms Therefore, Tom\u00e1s should buy 20 kilograms of trail mix for the entire trip. #### 20

Akua is preparing a traditional Nigerian dish, Jollof rice, for a party. The recipe requires a cylindrical cooking pot with a height of 20 cm and a radius of 15 cm. If the pot is filled to 75% capacity, how many liters of Jollof rice can Akua cook?

Let's break down the problem step by step: 1. First, we need to find the volume of the cylindrical cooking pot. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π (pi) is approximately 3.14159, r is the radius, and h is the height. Given that the radius (r) is 15 cm and the height (h) is 20 cm, we can plug these values into the formula to get the volume in cubic centimeters (cm^3). V = π * (15)^2 * 20 V = 3.14159 * 225 * 20 V = <<3.14159 * 225 * 20 = 14137.167>> cm^3 2. Since the pot is filled to 75% capacity, we need to calculate 75% of the total volume to find out how much Jollof rice Akua can cook. 75% of V = 0.75 * V 75% of V = 0.75 * 14137.167 75% of V = <<0.75 * 14137.167 = 10602.875>> cm^3 3. To convert the volume from cubic centimeters (cm^3) to liters, we use the conversion factor: 1 liter = 1000 cm^3. Volume in liters = 10602.875 cm^3 / 1000 Volume in liters = <<10602.875 / 1000 = 10.602875>> liters Therefore, Akua can cook approximately 10.602875 liters of Jollof rice. #### 10.6

Hans' family is planning a garden in their backyard. They want to plant a special type of flower that doubles in quantity every week. If they start with 8 flowers and want to know how many they will have in 6 weeks, how many flowers can they expect to have then?

Let's solve this step by step: 1. The flowers double in quantity every week. So, to find the number of flowers after 6 weeks, we need to calculate the number of flowers after each week. 2. Starting with 8 flowers, we calculate the number of flowers for each week: Week 1: 8 * 2 = <<8*2=16>>16 flowers Week 2: 16 * 2 = <<16*2=32>>32 flowers Week 3: 32 * 2 = <<32*2=64>>64 flowers Week 4: 64 * 2 = <<64*2=128>>128 flowers Week 5: 128 * 2 = <<128*2=256>>256 flowers Week 6: 256 * 2 = <<256*2=512>>512 flowers 3. Therefore, after 6 weeks, Hans' family can expect to have 512 flowers in their garden. #### 512

Tomás is planning a family reunion and needs to buy supplies. He has a budget of $150 for decorations, food, and drinks. Decorations cost $20, and food costs $60. If drinks come in packs of 12 for $10, how many packs of drinks can Tomás buy with the remaining budget?

Let's solve this step by step: 1. First, calculate the total amount spent on decorations and food: $20 (decorations) + $60 (food) = $<<20+60=80>>80 2. Subtract the amount spent from the total budget to find the remaining budget for drinks: $150 (total budget) - $80 (spent) = $<<150-80=70>>70 3. Determine how many packs of drinks Tomás can buy with the remaining budget: Since each pack costs $10, divide the remaining budget by the cost per pack: $70 ÷ $10 = <<70/10=7>>7 packs Therefore, Tomás can buy 7 packs of drinks with the remaining budget. #### 7

Tomás is planning a family reunion and wants to make sure he has enough seating for everyone. He has 15 tables that can seat 8 people each, but 3 tables are reserved for the catering staff. If he expects 25 more guests than the total number of people the remaining tables can seat, how many guests does he expect in total?

Let's break down the problem step by step: 1. First, calculate the total number of people the 15 tables can seat: 15 tables * 8 people/table = <<15*8=120>>120 people 2. Since 3 tables are reserved for the catering staff, subtract those tables from the total number of tables: 15 tables - 3 tables = <<15-3=12>>12 tables 3. Now, calculate the total number of people the remaining 12 tables can seat: 12 tables * 8 people/table = <<12*8=96>>96 people 4. Tomás expects 25 more guests than the total number of people the remaining tables can seat, so add 25 to the number of people the remaining tables can seat: 96 people + 25 people = <<96+25=121>>121 people Therefore, Tomás expects a total of 121 guests. #### 121

Trang is building a wooden birdhouse and needs to cut a rectangular piece of wood with an area of 48 square inches. If the length of the rectangle must be 8 inches, what should be the width of the rectangle to minimize the amount of wood used while meeting the area requirement?

To find the width of the rectangle that minimizes the amount of wood used while meeting the area requirement, let's follow these steps: 1. Understand that the area of a rectangle is given by the formula: Area = length * width. 2. We are given that the area must be 48 square inches and the length must be 8 inches. 3. We can substitute these values into the area formula to find the required width: 48 = 8 * width. 4. To find the width, we divide both sides of the equation by 8: width = 48 / 8. 5. Calculate the width: <<48 / 8 = 6>>. 6. Therefore, the width of the rectangle must be 6 inches to meet the area requirement of 48 square inches with a length of 8 inches. #### 6

Fatima is building a scale model of the Burj Khalifa for her school's art fair. The actual Burj Khalifa is 828 meters tall. If Fatima's model is 1/1000th the size of the real building, and she has already built 400 millimeters of it, how many more millimeters does she need to add to complete the model?

To find out how many more millimeters Fatima needs to add, let's first determine the total height of the model. The actual Burj Khalifa is 828 meters tall, and Fatima's model is 1/1000th of that size. 1. Convert the actual height of the Burj Khalifa to millimeters, since the model's height is given in millimeters. There are 1000 millimeters in a meter, so: 828 meters * 1000 millimeters/meter = <<828*1000=828000>>828,000 millimeters 2. Now, find the height of the model by taking 1/1000th of the actual Burj Khalifa's height in millimeters: 828,000 millimeters / 1000 = <<828000/1000=828>>828 millimeters 3. Fatima has already built 400 millimeters of the model. To find out how many more millimeters she needs to add, subtract the built height from the total model height: 828 millimeters - 400 millimeters = <<828-400=428>>428 millimeters Therefore, Fatima needs to add 428 millimeters to complete the model. #### 428

Nong is building a rectangular model garden bed that is 5 meters long and 3 meters wide. If she wants to put a path that is 1 meter wide around the entire garden bed, what is the area of the path?

To find the area of the path, we first need to find the total area of the larger rectangle that includes the garden bed and the path, and then subtract the area of the garden bed itself. Step 1: Find the dimensions of the larger rectangle. The length of the larger rectangle is the length of the garden bed plus twice the width of the path: 5 meters + 2 * 1 meter = <<5 + 2 * 1 = 7>>7 meters. The width of the larger rectangle is the width of the garden bed plus twice the width of the path: 3 meters + 2 * 1 meter = <<3 + 2 * 1 = 5>>5 meters. Step 2: Calculate the area of the larger rectangle and the garden bed, and then find the area of the path. The area of the larger rectangle is length * width = 7 meters * 5 meters = <<7 * 5 = 35>>35 square meters. The area of the garden bed is length * width = 5 meters * 3 meters = <<5 * 3 = 15>>15 square meters. The area of the path is the area of the larger rectangle minus the area of the garden bed: 35 square meters - 15 square meters = <<35 - 15 = 20>>20 square meters. #### 20

Nong is building a miniature replica of a traditional Thai house for a school project. The scale model will have a rectangular base with an area of 120 square centimeters and a length that is 4 centimeters more than its width. What is the width of the base of Nong's model house?

Let's solve this step-by-step: 1. Define the variables: Let w be the width of the base in centimeters. 2. The length is 4 centimeters more than the width, so the length is w + 4. 3. The area of a rectangle is given by the formula length * width. We are given that the area is 120 square centimeters, so we can write the equation: (w + 4) * w = 120 4. Expand and simplify the equation: w^2 + 4w = 120 Rearrange the equation to set it to 0: w^2 + 4w - 120 = 0 Factor the quadratic equation: (w + 12)(w - 10) = 0 5. Solve for w: w + 12 = 0 gives w = -12, which is not valid in this context. w - 10 = 0 gives w = 10. So, the width of the base is 10 centimeters. #### 10

Sergei observes the migration patterns of birds near Lake Baikal in Russia. If a flock of birds flies 15 meters in 3 seconds, and another flock flies 25 meters in 5 seconds, what is the difference in their average speeds in meters per second?

Let's solve this step by step: 1. First, let's calculate the average speed of the first flock of birds: Average speed = Total distance / Total time = 15 meters / 3 seconds = <<15/3=5>>5 meters/second 2. Next, let's calculate the average speed of the second flock of birds: Average speed = Total distance / Total time = 25 meters / 5 seconds = <<25/5=5>>5 meters/second 3. Now, we need to find the difference in their average speeds: Difference = Average speed of the second flock - Average speed of the first flock = 5 - 5 = <<5-5=0>>0 meters/second Therefore, there is no difference in the average speeds of the two flocks of birds. #### 0

Rohan and his friends are planning a camping trip in the Himalayas. They want to buy a new tent that is on sale for 15% off the original price of ₹25,000. However, there is an additional 5% discount for students. If Rohan has a 10% cashback coupon that he can use on the final discounted price, how much will he end up paying for the tent?

To solve this problem, let's break it down into steps: 1. First, calculate the price after the initial 15% discount: The original price of the tent is ₹25,000. Discount = 15% of ₹25,000 = <<15/100 * 25000 = 3750>>₹3,750. Price after the first discount = ₹25,000 - ₹3,750 = <<25000 - 3750 = 21250>>₹21,250. 2. Next, calculate the price after the additional 5% discount for students: Additional discount = 5% of ₹21,250 = <<5/100 * 21250 = 1062.5>>₹1,062.5. Price after the second discount = ₹21,250 - ₹1,062.5 = <<21250 - 1062.5 = 20187.5>>₹20,187.5. 3. Now, calculate the final price after applying the 10% cashback coupon: Cashback = 10% of ₹20,187.5 = <<10/100 * 20187.5 = 2018.75>>₹2,018.75. Final price = ₹20,187.5 - ₹2,018.75 = <<20187.5 - 2018.75 = 18168.75>>₹18,168.75. Therefore, Rohan will end up paying ₹18,168.75 for the tent. #### 18168.75

François Dupont, a professional rugby player from France, invested €15,000 in a high-yield savings account that earns a 4% annual interest rate compounded quarterly. If he doesn't make any withdrawals or deposits for 5 years, how much money will he have in his account at the end of the 5th year?

Let's break this down step by step: 1. First, we need to convert the annual interest rate to a quarterly rate since the interest is compounded quarterly: Quarterly rate = 4% / 4 = <<4/4=1>>1% per quarter 2. Next, we calculate the number of quarters in 5 years: Number of quarters = 5 years * 4 quarters/year = <<5*4=20>>20 quarters 3. Now, we can use the formula for compound interest to find the future value of François' investment: A = P(1 + r/n)^(nt) Where: A = the future value of the investment/loan, including interest P = principal investment amount (the initial deposit or loan amount) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = number of years the money is invested or borrowed for Plugging in the values, we get: A = 15000(1 + 0.01)^(20) A = 15000(1.01)^20 4. Calculate (1.01)^20: (1.01)^20 = <<1.01^20=1.2206503>>1.2206503 5. Now, multiply the principal amount by this result: A = 15000 * 1.2206503 = <<15000*1.2206503=18309.7545>>18309.7545 6. Round the result to two decimal places since we're dealing with euros: A ≈ 18309.75 7. Therefore, François will have approximately €18309.75 in his account at the end of the 5th year. #### 18309.75

In the Israeli Basketball League, the Maccabi Tel Aviv team has a 60% chance of winning against Hapoel Jerusalem. If they play two games, what is the probability that Maccabi Tel Aviv wins the first game but loses the second game?

To find the probability that Maccabi Tel Aviv wins the first game but loses the second game, we need to calculate the probability of each event happening separately and then multiply them together. 1. The probability of Maccabi Tel Aviv winning the first game is given as 60%, which can be expressed as 0.6 in decimal form. 2. The probability of Maccabi Tel Aviv losing the second game is the complement of winning, which is 1 - 0.6 = <<1 - 0.6 = 0.4>>. 3. Since these are independent events (the outcome of one game does not affect the other), we multiply the probabilities of each event happening: Probability = Probability of winning the first game * Probability of losing the second game 4. Calculate the combined probability: Probability = 0.6 * 0.4 = <<0.6 * 0.4 = 0.24>> 5. Therefore, the probability that Maccabi Tel Aviv wins the first game but loses the second game is 0.24 or 24%. #### 0.24

During the Cherry Blossom Festival in Tokyo, a popular food stall sells an average of 300 yakitori (grilled chicken skewers) per day. The stall operates for the 10 days of the festival, and the owner wants to optimize his production to meet the increasing demand, which grows by 10% each day. If he starts with 250 yakitori on the first day, how many yakitori should he produce on the tenth day to meet the demand, given that any unsold yakitori are donated to a local food bank?

To solve this problem, we first need to calculate the demand for yakitori on each day, taking into account the 10% growth rate. Then, we'll determine how many yakitori the owner should produce on the tenth day to meet this demand. 1. The initial demand is 250 yakitori on the first day. 2. The demand grows by 10% each day. To calculate the demand on the second day, we multiply the initial demand by 1.10 (100% + 10% growth). Second-day demand = 250 * 1.10 = <<250*1.10=275>>275 yakitori 3. We continue this process for each of the 10 days, calculating the demand for each day by multiplying the previous day's demand by 1.10. Third-day demand = 275 * 1.10 = <<275*1.10=302.5>>302.5 yakitori Fourth-day demand = 302.5 * 1.10 = <<302.5*1.10=332.75>>332.75 yakitori Fifth-day demand = 332.75 * 1.10 = <<332.75*1.10=366.025>>366.025 yakitori Sixth-day demand = 366.025 * 1.10 = <<366.025*1.10=402.6275>>402.6275 yakitori Seventh-day demand = 402.6275 * 1.10 = <<402.6275*1.10=442.89025>>442.89025 yakitori Eighth-day demand = 442.89025 * 1.10 = <<442.89025*1.10=487.179275>>487.179275 yakitori Ninth-day demand = 487.179275 * 1.10 = <<487.179275*1.10=535.8972025>>535.8972025 yakitori Tenth-day demand = 535.8972025 * 1.10 = <<535.8972025*1.10=589.48702275>>589.48702275 yakitori 4. Since the owner wants to meet the demand exactly and any unsold yakitori are donated, he should produce 589 yakitori on the tenth day (rounding the demand to the nearest whole number as you cannot produce a fraction of a yakitori). #### 589

Fatima wants to make a special dessert for Eid al-Fitr. The recipe calls for a ratio of 3 cups of flour to 2 cups of sugar. If Fatima has 9 cups of flour, how many cups of sugar should she use?

Let's solve this step by step: 1. First, we need to identify the ratio of flour to sugar in the recipe, which is 3:2. 2. Since Fatima has 9 cups of flour, we can set up a proportion to find out how many cups of sugar she needs: 3 cups of flour / 2 cups of sugar = 9 cups of flour / x cups of sugar. 3. To solve for x, we can cross-multiply and then divide: 3x = 9 * 2, so x = 9 * 2 / 3 = <<9*2/3=6>>6 cups of sugar. Therefore, Fatima should use 6 cups of sugar. #### 6

Mei is planning a road trip from Beijing to Shanghai, a distance of 1200 km. Her car can travel 400 km on a full tank of gas, and gas costs 7 yuan per liter. Each liter of gas allows her to travel 10 km. If she wants to minimize her gas expenses, how many liters of gas should she buy for the entire trip?

Let's solve this step by step: 1. First, calculate the total amount of gas Mei needs for the trip: Since her car can travel 400 km on a full tank and the total distance is 1200 km, she will need: 1200 km / 400 km per tank = <<1200 / 400 = 3>>3 full tanks of gas. 2. Since each liter of gas allows her to travel 10 km, the total liters needed for the trip is: Total distance / Distance per liter = 1200 km / 10 km per liter = <<1200 / 10 = 120>>120 liters 3. To minimize gas expenses, Mei should buy exactly the amount needed for the trip, which is 120 liters. Therefore, Mei should buy 120 liters of gas for the entire trip. #### 120

Maria is making tamales for her family's holiday dinner. Her recipe makes 24 tamales and requires a ratio of 2 cups of masa harina to 3 cups of pork filling. If she wants to triple the recipe, how many cups of masa harina and pork filling will she need in total?

To find the total amount of masa harina and pork filling needed, we'll follow these steps: 1. First, we need to triple the original ratio of 2 cups of masa harina to 3 cups of pork filling. To do this, we'll multiply both parts of the ratio by 3: - Masa harina: 2 cups * 3 = <<2*3=6>>6 cups - Pork filling: 3 cups * 3 = <<3*3=9>>9 cups 2. Since the original recipe makes 24 tamales, tripling the recipe will make 24 * 3 = <<24*3=72>>72 tamales. 3. The question asks for the total amount of masa harina and pork filling needed. We've already found these amounts in step 1. 4. To find the total amount of ingredients needed, we add the amounts of masa harina and pork filling: - Total ingredients = 6 cups (masa harina) + 9 cups (pork filling) = <<6+9=15>>15 cups Therefore, Maria will need 6 cups of masa harina and 9 cups of pork filling, for a total of 15 cups of ingredients. #### 15

Sergei observes that his pet rabbit, Masha, eats 3/4 of a bag of hay in 2 days. If he wants to buy enough hay for 6 days and each bag costs 250 rubles, how much will he spend in total?

To find out how much Sergei will spend in total, we need to calculate how many bags of hay Masha will eat in 6 days and then multiply that by the cost per bag. 1. First, let's determine how much hay Masha eats in one day: Masha eats 3/4 of a bag in 2 days, so in one day she eats 3/4 / 2 = 3/8 of a bag <<3/4 / 2 = 3/8>>. 2. Now, calculate how many bags Masha will eat in 6 days: Since Masha eats 3/8 of a bag per day, in 6 days she will eat 6 * 3/8 = 18/8 = 2.25 bags <<6 * 3/8 = 2.25>>. 3. Since we cannot buy a fraction of a bag, we round up to the nearest whole number to ensure Masha has enough hay for the entire 6 days. However, the problem does not explicitly state to round up or down, and the calculation gives us the exact amount needed. Thus, we proceed with 2.25 bags for the sake of calculation, acknowledging in real scenarios we'd likely round up to 3 bags for practicality. 4. Calculate the total cost by multiplying the number of bags needed by the cost per bag: Total cost = 2.25 bags * 250 rubles/bag = 562.5 rubles <<2.25 * 250 = 562.5>>. Therefore, Sergei will spend a total of 562.5 rubles on hay for Masha for 6 days. #### 562.5

Mrs. Cohen, a teacher at an Israeli high school, is preparing materials for her class. She wants to make sure each student gets an equal number of colored pencils for an art project. If she has 480 pencils to distribute among 8 classes, and each class has 20 students, how many pencils will each student receive?

Let's solve this step by step: 1. First, we need to find out how many pencils each class will receive. To do this, we divide the total number of pencils by the number of classes: 480 pencils / 8 classes = <<480/8=60>>60 pencils per class. 2. Now that we know each class gets 60 pencils, we need to find out how many pencils each student will receive. We do this by dividing the number of pencils per class by the number of students in each class: 60 pencils / 20 students = <<60/20=3>>3 pencils per student. Therefore, each student will receive 3 pencils. #### 3

Ji-Hyun is making a traditional Korean dessert called Yakgwa for her family gathering. The recipe requires 3/4 cup of honey. If she wants to make half the amount of Yakgwa, how much honey will she need?

To find out how much honey Ji-Hyun will need for half the amount of Yakgwa, we need to multiply the original amount of honey by 1/2. First, let's convert 3/4 into a decimal to make the calculation easier: 3/4 = <<3/4=0.75>>0.75. Now, we multiply 0.75 by 1/2 to find the amount of honey needed for half the recipe: 0.75 * 1/2 = 0.75 * 0.5 = <<0.75*0.5=0.375>>0.375. To express this as a fraction, we can simplify it: 0.375 = 3/8 = <<3/8=0.375>>3/8. Therefore, Ji-Hyun will need 3/8 cup of honey to make half the amount of Yakgwa.#### 0.375

Adebayo bought 3 bags of rice for 900 naira. If he wants to buy 5 bags of rice, how much will he pay in total?

To find the total cost of 5 bags of rice, we need to first find the cost of one bag of rice and then multiply it by 5. 1. First, find the cost of one bag of rice by dividing the total cost of 3 bags by 3: 900 naira / 3 bags = <<900/3=300>>300 naira per bag 2. Now, multiply the cost of one bag by 5 to find the total cost of 5 bags: 300 naira per bag * 5 bags = <<300*5=1500>>1500 naira Therefore, Adebayo will pay a total of 1500 naira for 5 bags of rice. #### 1500

Mei wants to buy a new rug for her bedroom that is shaped like a rectangle. If the rug is 8 meters long and 5 meters wide, and the price of the rug is $15 per square meter, how much will Mei pay for the rug?

To find the total cost of the rug, we first need to calculate its area. The area of a rectangle is calculated as length times width. In this case, the length is 8 meters and the width is 5 meters. 1. Calculate the area of the rug: Area = length * width Area = 8 * 5 <<8 * 5 = 40>> square meters 2. Now, we multiply the area by the price per square meter to find the total cost: Total cost = Area * price per square meter Total cost = 40 * 15 <<40 * 15 = 600>> dollars Therefore, Mei will pay $600 for the rug. #### 600

Mei and her brother, Jian, are saving money for a family trip to Shanghai. Mei has saved $120 and Jian has saved $80. If their parents will give them an additional $50 to help with the trip, how much money will they have in total?

Let's solve this step by step: 1. First, calculate the total amount of money Mei and Jian have saved: Mei has saved $120 and Jian has saved $80, so together they have: <<120 + 80 = 200>>$ 2. Then, add the additional $50 their parents will give them: <<200 + 50 = 250>>$ Therefore, they will have a total of $250 for the trip. #### 250

Min-ju's family is preparing for the Korean New Year, Seollal. They want to package 480 traditional sweets into boxes that hold 8 sweets each. How many boxes can they fill?

Let's solve this step by step: 1. We know the total number of sweets Min-ju's family wants to package is 480. 2. Each box can hold 8 sweets. 3. To find out how many boxes they can fill, we need to divide the total number of sweets by the number of sweets each box can hold: <<480 / 8 = 60>> Therefore, Min-ju's family can fill 60 boxes with the traditional sweets. #### 60

Akua is preparing a traditional Ghanaian dish, Groundnut Soup, for a large family gathering. The recipe requires a cylindrical clay pot that is 20 inches in diameter and 15 inches deep. If the soup needs to be 3/4 of the pot's volume, and Akua wants to serve the soup in bowls that hold 2/5 of a cubic inch each, how many bowls can she fill with the Groundnut Soup?

To find out how many bowls Akua can fill, we first need to calculate the volume of the soup in the pot and then divide it by the volume of each bowl. 1. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Since the diameter is given, we first find the radius: Radius = diameter / 2 = 20 / 2 = <<20/2=10>>10 inches 2. Now, calculate the volume of the entire pot: Volume = π * (10)^2 * 15 = <<3.14159 * 10^2 * 15 = 4712.39>> cubic inches 3. The soup fills 3/4 of the pot's volume: Volume of soup = 3/4 * Volume of pot = 3/4 * 4712.39 = <<3/4 * 4712.39 = 3534.29>> cubic inches 4. Each bowl holds 2/5 of a cubic inch. To find out how many bowls can be filled, divide the volume of the soup by the volume of each bowl: Number of bowls = Volume of soup / Volume of each bowl = 3534.29 / (2/5) = 3534.29 / 0.4 = <<3534.29 / 0.4 = 8835.725>> Since we can't fill a fraction of a bowl and the number of bowls must be a whole number, we round down to the nearest whole number because you can't fill a fraction of a bowl. Therefore, Akua can fill 8835 bowls with the Groundnut Soup. #### 8835

The Okoro family is planning a traditional Nigerian dinner for their community. They need to make a special sauce that requires a ratio of 3 tablespoons of peanut paste to 5 tablespoons of vegetable oil. If they want to make 24 batches of the sauce and they already have 120 tablespoons of peanut paste, how many tablespoons of vegetable oil will they need in total?

Let's break this down step by step: 1. First, we need to determine how many tablespoons of peanut paste are needed for 24 batches of the sauce. Since they already have 120 tablespoons of peanut paste, we can use this information to find out how many batches they can make with the given amount. However, the problem states they want to make 24 batches, so we actually need to find out how much vegetable oil is required for these batches. 2. Given the ratio is 3 tablespoons of peanut paste to 5 tablespoons of vegetable oil, for every 3 tablespoons of peanut paste, we need 5 tablespoons of vegetable oil. 3. We know that they want to make 24 batches, but we don't know how much peanut paste is needed for 24 batches. Since we have the ratio 3:5, we can set up a proportion to find the amount of peanut paste needed for 24 batches. However, we already have 120 tablespoons of peanut paste and the ratio of peanut paste to vegetable oil is 3:5. So, we can directly use the given amount of peanut paste to find the amount of vegetable oil needed. 4. To find the amount of vegetable oil needed, we can first find how many sets of 3 tablespoons of peanut paste there are in 120 tablespoons. 120 / 3 = <<120/3=40>>40 sets of 3 tablespoons of peanut paste. 5. Since the ratio of peanut paste to vegetable oil is 3:5, we can multiply the number of sets of 3 tablespoons of peanut paste by 5 to find the amount of vegetable oil needed. 40 sets * 5 tablespoons/set = <<40*5=200>>200 tablespoons of vegetable oil. 6. However, this is the amount of vegetable oil needed for the given amount of peanut paste, which makes 40 sets. Since they want to make 24 batches, we need to find how many sets of 3 tablespoons of peanut paste are needed for 24 batches. Given the ratio 3:5, for every batch, we need 3 tablespoons of peanut paste. 24 batches * 3 tablespoons/batch = <<24*3=72>>72 tablespoons of peanut paste. 7. Now, we can find how many sets of 3 tablespoons of peanut paste are needed for 24 batches. 72 tablespoons / 3 tablespoons/set = <<72/3=24>>24 sets of 3 tablespoons of peanut paste. 8. Since the ratio of peanut paste to vegetable oil is 3:5, we can multiply the number of sets of 3 tablespoons of peanut paste by 5 to find the amount of vegetable oil needed for 24 batches. 24 sets * 5 tablespoons/set = <<24*5=120>>120 tablespoons of vegetable oil. Therefore, the Okoro family will need 120 tablespoons of vegetable oil in total for 24 batches of the sauce. #### 120

Gal is making a traditional Israeli dish, shakshuka, for her family dinner. She needs to adjust the recipe for 8 people instead of the original 4 people it serves. If the original recipe calls for 2 large onions and there's a 20% chance an onion is rotten inside, what's the probability that Gal will have at least one good onion for her scaled-up recipe?

Let's solve this step by step: 1. First, we need to determine how many onions Gal needs for her scaled-up recipe. Since the original recipe calls for 2 onions for 4 people, and she's scaling it up for 8 people, we can find the number of onions needed by multiplying the original amount by 2 (since 8 is twice 4): <<2 * 2 = 4>> So, Gal needs 4 onions for her scaled-up recipe. 2. Given that there's a 20% chance an onion is rotten inside, we want to find the probability that at least one onion is good. To simplify this, we'll find the probability that all onions are rotten and subtract that from 1 (since the sum of the probability of an event happening and the probability of it not happening is 1). The probability that an onion is rotten is 20%, or 0.2. The probability that all 4 onions are rotten is: 0.2 * 0.2 * 0.2 * 0.2 = <<0.2 * 0.2 * 0.2 * 0.2 = 0.0016>> So, the probability that at least one onion is good is 1 minus the probability that all onions are rotten: 1 - 0.0016 = <<1 - 0.0016 = 0.9984>> Therefore, the probability that Gal will have at least one good onion for her scaled-up recipe is 99.84%. #### 0.9984

Fatima is planning a rectangular garden in her backyard to plant flowers for her pet rabbits. The garden will be 8 meters long and 5 meters wide. If she wants to put a fence around the entire garden, and the fencing costs 10 dirhams per meter, how much will it cost her to fence the garden?

Let's solve this step by step: 1. First, we need to find the perimeter of the garden since Fatima wants to fence the entire area. The formula for the perimeter of a rectangle is P = 2(length + width). 2. Given the length is 8 meters and the width is 5 meters, we can substitute these values into the formula: P = 2(8 + 5). 3. Calculate the sum inside the parentheses first: 8 + 5 = <<8+5=13>>13. 4. Then, multiply the sum by 2 to find the perimeter: 2 * 13 = <<2*13=26>>26 meters. 5. Knowing the perimeter and the cost per meter of fencing (10 dirhams), we can find the total cost by multiplying the perimeter by the cost per meter: 26 meters * 10 dirhams/meter = <<26*10=260>>260 dirhams. Therefore, it will cost Fatima 260 dirhams to fence the garden. #### 260

Nong's family is building a rectangular garden in their backyard. The length of the garden is 8 meters, and the width is 5 meters. If they want to put a fence around the garden, what is the total length of the fence they need to buy?

To find the total length of the fence needed, we must calculate the perimeter of the garden. The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width). 1. First, we add the length and the width together: 8 meters + 5 meters = <<8+5=13>>13 meters. 2. Then, we multiply the sum by 2 to get the perimeter: 2 * 13 meters = <<2*13=26>>26 meters. Therefore, the total length of the fence Nong's family needs to buy is 26 meters. #### 26

Fatima and her friends are planning a camping trip in the desert. They want to share some dates as a snack. If they have 3/4 of a box of dates and they want to divide it equally among 6 people, but then 2 more friends join, how many dates will each person get if there are 36 dates in a full box?

Let's solve this step by step: 1. First, we need to find out how many dates Fatima and her friends have in total. Since they have 3/4 of a box and there are 36 dates in a full box, we calculate the total number of dates they have: 3/4 * 36 = <<3/4*36=27>>27 dates 2. Initially, they want to divide these dates among 6 people. However, 2 more friends join, making the total number of people 6 + 2 = <<6+2=8>>8 3. To find out how many dates each person will get, we divide the total number of dates by the total number of people: 27 dates / 8 people = <<27/8=3.375>>3.375 dates per person Since you can't divide dates into fractions, we'll consider the whole number part, which means each person will get 3 dates. #### 3

The Kuznetsov family is planning a garden in their backyard in Moscow. They want to create a rectangular garden with a length that is 5 meters more than its width. If they have 60 meters of fencing to enclose the garden, what should be the width of the garden to maximize its area?

Let's solve this problem step by step: 1. Let's denote the width of the garden as w. Since the length is 5 meters more than the width, the length can be represented as w + 5. 2. The perimeter of a rectangle is given by the formula P = 2(length + width). We are given that the perimeter (the fencing) is 60 meters. So, we can set up the equation: 60 = 2(w + (w + 5)). 3. Simplify the equation: 60 = 2(2w + 5). 4. Distribute the 2: 60 = 4w + 10. 5. Subtract 10 from both sides to isolate terms with w: 60 - 10 = 4w + 10 - 10, which simplifies to 50 = 4w. 6. Divide both sides by 4 to solve for w: 50 / 4 = 4w / 4, resulting in w = 12.5. 7. Now that we know the width is 12.5 meters, we can find the length: length = w + 5 = 12.5 + 5 = 17.5 meters. 8. To ensure this maximizes the area, we can check the area using the formula A = length * width: A = 17.5 * 12.5 = 218.75 square meters. Given the constraints, this will indeed maximize the area because it uses all the available fencing efficiently, creating a rectangle where the difference between length and width is exactly 5 meters as required. #### 12.5

Ayşe has been saving money for a new phone and has 850 Turkish Lira in her piggy bank. She earns an extra 150 Lira by walking her neighbor's dog. How much money does Ayşe have now to spend on the phone?

Let's solve this step by step: 1. Ayşe starts with 850 Turkish Lira. 2. She earns an extra 150 Lira by walking her neighbor's dog. 3. To find the total amount of money Ayşe has now, we add the initial amount and the extra earnings: <<850 + 150 = 1000>> Therefore, Ayşe has 1000 Turkish Lira to spend on the phone. #### 1000

Kanchana finds a beehive with 150 bees in it. Over the next month, the number of bees increases by 15%. Then, due to environmental changes, the number decreases by 8%. How many bees are in the hive now?

To find the final number of bees in the hive, we'll follow these steps: 1. Calculate the increase in the number of bees: Initial number of bees = 150 Increase percentage = 15% Increase in bees = 15% of 150 = <<15/100*150=22.5>>22.5 bees 2. Calculate the total number of bees after the increase: New number of bees = Initial number of bees + Increase in bees = 150 + 22.5 = <<150+22.5=172.5>>172.5 bees 3. Calculate the decrease in the number of bees: Decrease percentage = 8% Decrease in bees = 8% of 172.5 = <<8/100*172.5=13.8>>13.8 bees 4. Calculate the final number of bees after the decrease: Final number of bees = New number of bees - Decrease in bees = 172.5 - 13.8 = <<172.5-13.8=158.7>>158.7 bees Since we can't have a fraction of a bee, we'll round the final number of bees to the nearest whole number. However, the task does not explicitly ask for rounding, so we will provide the precise calculation result. #### 158.7

Mrs. Singh is planning a school fundraiser in her grade 6 class in Toronto. She ordered 200 samosas to sell at the event, with a plan to sell them at a 25% markup to make a profit. However, due to a mistake, 15% of the samosas were damaged during delivery. If she wants to make at least $150 in profit, how much should she sell each undamaged samosa for?

Let's break this down step by step: 1. First, calculate the number of undamaged samosas: 15% of 200 samosas were damaged, so the number of damaged samosas is: <<15/100 * 200 = 30>>30 samosas Therefore, the number of undamaged samosas is: 200 - 30 = <<200 - 30 = 170>>170 samosas 2. Mrs. Singh wants to make at least $150 in profit. Since she's selling the samosas at a 25% markup, this profit will come from the 25% increase in price. 3. Let's assume the original price of each samosa (the price Mrs. Singh paid for it) is x dollars. Then, the selling price will be x + 25% of x. 4. The total profit Mrs. Singh wants to make is $150. This profit comes from selling 170 samosas at a 25% markup, so we can set up the equation: Total Profit = (Selling Price - Original Price) * Number of Samosas 150 = (x + 25% of x - x) * 170 5. Simplify the equation: 150 = (0.25x) * 170 150 = 42.5x 6. Solve for x: x = 150 / 42.5 x = <<150 / 42.5 = 3.5294117647059>>3.5294117647059 Since the original price must be a reasonable amount, we can round this value. Let's assume the original price is approximately $3.53. 7. Calculate the selling price with a 25% markup: Selling Price = Original Price + 25% of Original Price Selling Price = 3.53 + 0.25 * 3.53 Selling Price = 3.53 + <<0.25 * 3.53 = 0.8825>>0.8825 Selling Price = <<3.53 + 0.8825 = 4.4125>>4.4125 Rounding to two decimal places, the selling price should be approximately $4.41. 8. Verify the profit: Total Profit = (Selling Price - Original Price) * Number of Samosas Total Profit = (4.41 - 3.53) * 170 Total Profit = 0.88 * 170 Total Profit = <<0.88 * 170 = 149.6>>149.6 This is very close to the target profit of $150. Therefore, Mrs. Singh should sell each undamaged samosa for approximately $4.41 to make at least $150 in profit. #### 4.41

Hans' Oma gave him €500 for his birthday with the condition that he put it in a savings account that earns a 4% annual interest rate, compounded annually. If Hans doesn't withdraw any money, how much will he have in 3 years?

Let's solve this 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, r is the annual interest rate, and n is the number of years. 2. In this case, P = \u20ac500, r = 4% or 0.04, and n = 3 years. 3. Now, we can plug these values into the formula to find the amount after 3 years: A = 500(1 + 0.04)^3 = 500(1.04)^3 = 500 * <<1.04^3 = 1.125984>> = <<500 * 1.125984 = 562.992>> 4. Therefore, Hans will have approximately \u20ac562.99 in 3 years. #### 562.99

Tomoko scored 15 points in the first half of the basketball game and 8 points in the second half. If she made 7 three-pointers in total, and the rest of her points came from two-pointers, how many two-pointers did she make?

Let's break down the problem step by step: 1. First, let's find out how many points Tomoko scored in total: 15 points in the first half + 8 points in the second half = <<15+8=23>>23 points in total. 2. Since she made 7 three-pointers, the points from three-pointers would be 7 * 3 = <<7*3=21>>21 points. 3. To find out how many points came from two-pointers, we subtract the points from three-pointers from the total points: 23 - 21 = <<23-21=2>>2 points from two-pointers. 4. Since each two-pointer is worth 2 points, we divide the points from two-pointers by 2 to find the number of two-pointers: 2 / 2 = <<2/2=1>>1 two-pointer. Therefore, Tomoko made 1 two-pointer. #### 1

Ayşe's family traditionally gives her a lump sum of money on Nowruz, which she invests in a savings account with a 5% annual interest rate compounded annually. If she invests 1,000 Turkish lira and doesn't withdraw any money for 3 years, how much money will she have in her account after the interest is compounded at the end of the third year?

To find out how much money Ay\u015fe will have in her account after 3 years, we need to calculate the compound interest. Let's break it down step by step: 1. First, we need to calculate the interest for the first year: Interest for the first year = Principal amount * Interest rate = 1,000 Turkish lira * 5% = 1,000 * 0.05 = <<1000*0.05=50>>50 Turkish lira So, the total amount after the first year = Principal amount + Interest = 1,000 + 50 = <<1000+50=1050>>1,050 Turkish lira 2. Now, we calculate the interest for the second year: Interest for the second year = New principal amount * Interest rate = 1,050 Turkish lira * 5% = 1,050 * 0.05 = <<1050*0.05=52.5>>52.5 Turkish lira So, the total amount after the second year = New principal amount + Interest = 1,050 + 52.5 = <<1050+52.5=1102.5>>1,102.5 Turkish lira 3. Finally, we calculate the interest for the third year: Interest for the third year = New principal amount * Interest rate = 1,102.5 Turkish lira * 5% = 1,102.5 * 0.05 = <<1102.5*0.05=55.125>>55.125 Turkish lira So, the total amount after the third year = New principal amount + Interest = 1,102.5 + 55.125 = <<1102.5+55.125=1157.625>>1,157.625 Turkish lira Therefore, Ay\u015fe will have approximately 1,157.63 Turkish lira in her account after 3 years. #### 1157.63

During the Eid al-Fitr celebration, Aliyu's family is planning a big feast. They ordered 150 kilograms of jollof rice from a catering service, which offers a 15% discount for bulk orders above 100 kilograms. However, due to a misunderstanding, the catering service applied a 10% discount instead. How many more kilograms of jollof rice can Aliyu's family buy with the amount they saved if the original price per kilogram is ₦500 and they decide to spend the saved amount on additional jollof rice at the same price?

To find out how many more kilograms of jollof rice Aliyu's family can buy with the amount they saved, let's first calculate the amount they saved due to the discount mix-up. 1. Calculate the correct discount amount for the 15% discount on the original price of 150 kilograms of jollof rice at \u20a6500 per kilogram: Original price = 150 kilograms * \u20a6500/kilogram = \u20a6975000 Correct discount = 15% of \u20a6975000 = <<15/100*975000=146250>>\u20a6146250 2. Calculate the incorrect discount amount applied (10% of the original price): Incorrect discount = 10% of \u20a6975000 = <<10/100*975000=97500>>\u20a697500 3. Calculate the difference in the discount amounts to find the additional amount saved: Additional amount saved = Correct discount - Incorrect discount = \u20a6146250 - \u20a697500 = \u20a648750 4. Calculate how many kilograms of jollof rice can be bought with the additional amount saved at the original price of \u20a6500 per kilogram: Additional kilograms = Additional amount saved / Price per kilogram = \u20a648750 / \u20a6500 = <<48750/500=97.5>>97.5 kilograms Since we can't buy a fraction of a kilogram, we round down to the nearest whole number, as you cannot purchase a fraction of a kilogram. Therefore, Aliyu's family can buy 97 more kilograms of jollof rice with the amount they saved. #### 97

Hans is baking a traditional German apple strudel for his family dinner. The recipe calls for 3/4 cup of sugar to make 8 servings. If Hans wants to make 12 servings, how many cups of sugar will he need?

Let's solve this step by step: 1. First, we need to find out how much sugar is needed per serving. The recipe requires 3/4 cup of sugar for 8 servings. To find the amount per serving, we'll divide the total amount of sugar by the number of servings: 3/4 cup / 8 servings = <<3/4 / 8 = 3/32>> cup per serving 2. Since Hans wants to make 12 servings, we'll multiply the amount of sugar per serving by the new number of servings to find the total amount needed: 3/32 cup per serving * 12 servings = <<3/32 * 12 = 9/8>> cups 3. To convert this improper fraction into a mixed number or decimal for easier understanding, we can divide the numerator by the denominator: 9 / 8 = <<9 / 8 = 1.125>> cups Therefore, Hans will need 1.125 cups of sugar for 12 servings. #### 1.125

The Vietnamese U16 soccer team has a ratio of 3 wins to every 5 games played. If they played a total of 20 games in the season, how many wins did they have?

Let's solve this step by step: 1. First, we need to establish the ratio of wins to total games played, which is 3 wins to 5 games. 2. Next, we find out how many sets of 5 games are there in 20 games: 20 games / 5 games per set = <<20/5=4>>4 sets 3. Now, we determine the number of wins in 4 sets: 3 wins per set * 4 sets = <<3*4=12>>12 wins 4. Therefore, the Vietnamese U16 soccer team had 12 wins. #### 12

During the Chinese New Year, a store in Beijing offers a series of discounts on traditional decorations. Initially, a set of lanterns is priced at 250 yuan. The store first offers a 15% discount for the holiday season. Then, for purchases over 200 yuan, an additional 8% discount is applied. If Sara also has a membership card that gives her another 5% off any purchase, how much will she pay for the set of lanterns?

Let's solve this step by step: 1. The initial price of the set of lanterns is 250 yuan. 2. The store offers a 15% discount for the holiday season. First, we find 15% of 250 yuan: 15% of 250 = <<15/100 * 250 = 37.5>>37.5 yuan. 3. Subtract the discount from the original price to get the price after the first discount: 250 - 37.5 = <<250 - 37.5 = 212.5>>212.5 yuan. 4. Since the purchase is over 200 yuan, an additional 8% discount is applied. Calculate 8% of 212.5: 8% of 212.5 = <<8/100 * 212.5 = 17>>17 yuan. 5. Subtract the additional discount from the price after the first discount to get the price after the second discount: 212.5 - 17 = <<212.5 - 17 = 195.5>>195.5 yuan. 6. Sara's membership card gives her another 5% off any purchase. Calculate 5% of 195.5: 5% of 195.5 = <<5/100 * 195.5 = 9.775>>9.775 yuan. 7. Subtract the membership discount from the price after the second discount to get the final price Sara will pay: 195.5 - 9.775 = <<195.5 - 9.775 = 185.725>>185.725 yuan. 8. Round the final price to two decimal places, as currency values typically are: 185.725 ≈ <<185.725 = 185.73>>185.73 yuan. Therefore, Sara will pay 185.73 yuan for the set of lanterns. #### 185.73

Tomer wants to buy gifts for his family members during Hanukkah. He has a budget of 500 shekels and wants to buy a combination of small and large menorahs. The small menorah costs 50 shekels and the large one costs 100 shekels. However, he also needs to consider the cost of candles, which is 20 shekels for the small menorah and 30 shekels for the large one. If he wants to buy at least 3 small menorahs and at most 2 large menorahs, how many of each type of menorah should he buy to maximize the total number of menorahs within his budget?

Let's break this down step by step: 1. Define variables: Let x be the number of small menorahs and y be the number of large menorahs. 2. Set up the total cost equation based on the given prices and the cost of candles: Total Cost = 50x + 20x + 100y + 30y Simplify the equation: Total Cost = 70x + 130y 3. Given Tomer's budget of 500 shekels, we can set up the inequality: 70x + 130y ≤ 500 4. Tomer also wants to buy at least 3 small menorahs and at most 2 large menorahs, so we have the constraints: x ≥ 3 y ≤ 2 5. Since x and y must be whole numbers (you can't buy part of a menorah), we look for integer solutions within these constraints that maximize the total number of menorahs (x + y). 6. Let's start with the minimum requirement for x, which is 3, and see how many large menorahs Tomer can afford: If x = 3, then 70*3 + 130y ≤ 500 Simplify: 210 + 130y ≤ 500 Subtract 210 from both sides: 130y ≤ 290 Divide by 130: y ≤ <<290/130=2.23>>2.23 Since y must be an integer and y ≤ 2, the maximum y can be in this case is 2. 7. Now, calculate the total cost if x = 3 and y = 2: Total Cost = 70*3 + 130*2 = 210 + 260 = <<210+260=470>>470 shekels This combination is within the budget, and since we're maximizing the number of menorahs, buying more small ones would not allow for more large ones due to budget constraints. Therefore, Tomer should buy 3 small menorahs and 2 large menorahs to maximize the total number of menorahs within his budget. #### 5

Mei is building a traditional Chinese kite for a cultural festival and needs to optimize the use of her materials. She has 120 meters of lightweight string for the kite's framework and tail. The framework requires 5 meters of string per meter of kite length, and the tail requires 2 meters of string per meter of tail length. If the kite's length must be between 10 and 15 meters and the tail's length must be between 5 and 10 meters, what is the maximum length of the kite Mei can build while still having enough string for a 6-meter tail?

Let's solve this step-by-step: 1. First, calculate the total string used for the kite's framework and tail combined, excluding the tail's length which we know will be 6 meters and thus requiring 6 * 2 = <<6*2=12>>12 meters of string. 2. This leaves us with 120 - 12 = <<120-12=108>>108 meters of string for the kite's framework and the variable part of the tail (which we don't need to worry about since the tail's length is given). 3. Since the framework requires 5 meters of string per meter of kite length, let's represent the kite's length by 'L'. The string used for the kite is then 5L. 4. We are given that the kite's length must be between 10 and 15 meters, but to maximize the kite's length, we want to use as much string as possible for the kite itself without exceeding the 108 meters available for the framework. 5. Setting up the equation to find the maximum length (L) given the constraints: 5L ≤ 108 6. Solving for L gives us: L ≤ 108 / 5 L ≤ <<108/5=21.6>>21.6 7. However, we are constrained by the problem statement that the kite's length must be between 10 and 15 meters. Thus, the maximum length within the allowed range is 15 meters, but since we're optimizing for maximum length without exceeding the string limit, we check if 15 meters is achievable with the string left after accounting for the tail. 8. Given that 15 meters is within our string limit (since 15 * 5 = <<15*5=75>>75 meters, which is less than 108 meters left after accounting for the tail), we confirm the maximum length of the kite that can be built is indeed 15 meters. #### 15

During Hanukkah, the Kagan family traditionally fries sufganiyot (jelly-filled doughnuts) for their holiday party. This year, they want to make a special batch using 3/4 cup of oil for every 2 1/3 cups of flour. If they have 6 cups of oil, how many cups of flour will they need to buy to make the sufganiyot for their 50 guests?

Let's solve this step by step: 1. First, we need to establish the ratio of oil to flour. The recipe calls for 3/4 cup of oil for every 2 1/3 cups of flour. 2. To find out how many cups of flour are needed for 6 cups of oil, we set up a proportion. Let x be the amount of flour needed for 6 cups of oil: (3/4) / (2 1/3) = 6 / x To solve for x, first convert the mixed number to an improper fraction: 2 1/3 = 7/3 Now, rewrite the proportion and solve for x: (3/4) / (7/3) = 6 / x Cross-multiply: (3/4) * x = 6 * (7/3) Simplify both sides: (3/4) * x = 14 Solve for x: x = 14 / (3/4) x = 14 * (4/3) x = <<14 * 4 / 3 = 18.67>> 3. Since we can't buy a fraction of a cup of flour and we're planning for 50 guests, we round up to the nearest whole number to ensure we have enough for everyone. However, in this case, understanding the context is crucial; the calculation gives us the amount needed for the recipe ratio, not necessarily for 50 guests. The question, however, directly asks how much flour is needed for the sufganiyot without specifying further adjustments for the number of guests. Therefore, we directly address the calculated need based on the oil amount: #### 18.67

Maya and her friends are planning a camping trip in the Canadian wilderness. They want to bring a certain type of bug repellent that comes in 100ml bottles. The active ingredient in the repellent decays at a rate of 20% per day. If they buy a bottle that contains 80% active ingredient on the day of purchase, what percentage of the active ingredient will remain after 2 days of camping?

Let's solve this step by step: 1. First, understand the decay rate of the active ingredient, which is 20% per day. 2. The initial concentration of the active ingredient is 80%. 3. Calculate the remaining active ingredient after the first day: 80% - (20% of 80%) = 80% - <<20 * 80 / 100 = 16>>% = <<80 - 16 = 64>>% 4. Now, calculate the remaining active ingredient after the second day, applying the same decay rate to the result from step 3: 64% - (20% of 64%) = 64% - <<20 * 64 / 100 = 12.8>>% = <<64 - 12.8 = 51.2>>% Therefore, after 2 days of camping, 51.2% of the active ingredient will remain. #### 51.2

Tomás has been saving money for a new bike and has $120 in his piggy bank. Every month, he earns $15 by walking his neighbor's dog and $8 by helping his mom with extra chores. However, he also spends $5 each month on snacks and small toys. If Tomás wants to buy a bike that costs $250, how many months will it take him to save enough money?

Let's break this down step by step: 1. Tomás starts with $120 in his piggy bank. 2. Each month, he earns $15 by walking his neighbor's dog and $8 by helping his mom with extra chores, for a total of: $15 + $8 = <<15+8=23>>$23 per month. 3. However, he also spends $5 each month on snacks and small toys, so his net earnings per month are: $23 - $5 = <<23-5=18>>$18. 4. To find out how many months it will take Tomás to save enough money, we need to subtract the amount he already has from the price of the bike: $250 - $120 = <<250-120=130>>$130. 5. Now, we divide the amount he still needs by his monthly net earnings: $130 ÷ $18 = <<130/18=7.22>>7.22 months. 6. Since Tomás can't save a fraction of a month, we round up to the nearest whole number to ensure he has enough money: 7.22 → 8 months. Therefore, it will take Tomás 8 months to save enough money to buy the bike. #### 8

Akua is planning a road trip from Accra to Kumasi in Ghana. The distance between the two cities is 200 km. If her car's fuel tank can hold 50 liters of petrol and the car consumes 10 liters of petrol per 50 km, what percentage of the fuel tank will be used for the entire trip?

Let's solve this step by step: 1. First, we need to find out how many liters of petrol the car will consume for the entire trip. Since the car consumes 10 liters of petrol per 50 km, we divide the total distance by 50 km to find how many times 50 km fits into the total distance: 200 km / 50 km = <<200/50=4>>4. 2. Then, we multiply the number of times 50 km fits into the total distance by the amount of petrol consumed per 50 km to find the total amount of petrol consumed for the entire trip: 4 * 10 liters = <<4*10=40>>40 liters. 3. Now, we need to find the percentage of the fuel tank that will be used for the entire trip. To do this, we divide the amount of petrol consumed by the capacity of the fuel tank and then multiply by 100 to convert it into a percentage: (40 liters / 50 liters) * 100 = <<40/50*100=80>>80%. Therefore, 80% of the fuel tank will be used for the entire trip. #### 80