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question:Cindy can jump rope for 12 minutes before tripping up on the ropes. Betsy can jump rope x% as long as Cindy before tripping up, while Tina can jump three times as long as Betsy. Tina can jump rope 6 more minutes than Cindy. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the percentage of time Betsy can jump rope compared to Cindy. We know that Cindy can jump rope for 12 minutes before tripping up, and Tina can jump rope 6 more minutes than Cindy. Therefore, Tina can jump rope for 12 + 6 = 18 minutes. We also know that Tina can jump three times as long as Betsy. Therefore, Betsy can jump rope for 18 / 3 = 6 minutes. To find the percentage of time Betsy can jump rope compared to Cindy, we divide Betsy's time by Cindy's time and multiply by 100: (x/100) * 12 = 6 To solve for x, we divide both sides of the equation by 12 and multiply by 100: x/100 = 6/12 x/100 = 1/2 x = 50 The value of x is 50. 50 The answer is: 50
question:f a + 4b = 33 and 6a + 3b = 51, what is the value of a + b?
answer:We can solve this system of equations by elimination. Multiplying the first equation by 3 and the second equation by 4, we get: 3(a + 4b) = 3(33) implies 3a + 12b = 99 4(6a + 3b) = 4(51) implies 24a + 12b = 204 Now, subtracting the first equation from the second equation, we eliminate the 12b term: (24a + 12b) - (3a + 12b) = 204 - 99 implies 21a = 105 implies a = 5 Substituting this value of a into the first equation, we can solve for b: 5 + 4b = 33 implies 4b = 28 implies b = 7 Therefore, a + b = 5 + 7 = boxed{12}. The answer is: 12
question:A movie theatre has 250 seats. The cost of a ticket is x for an adult and 4 for a child. The theatre is full and contains 188 children. The total ticket revenue for this movie session is 1124. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the cost of a ticket for an adult. Let's break down the information given: Total number of seats in the theatre: 250 Number of children in the theatre: 188 Cost of a ticket for a child: 4 Total ticket revenue: 1124 We can set up the equation as follows: Number of adult tickets * Cost per adult ticket + Number of child tickets * Cost per child ticket = Total ticket revenue (250 - 188) * x + 188 * 4 = 1124 Let's simplify and solve for x: 62x + 752 = 1124 To isolate x, we subtract 752 from both sides of the equation: 62x + 752 - 752 = 1124 - 752 62x = 372 To solve for x, we divide both sides of the equation by 62: x = 372 / 62 x = 6 The value of x is 6. 6 The answer is: 6
question:Bob has to hire someone to fix his garden. A storm destroyed all 20 of his rose bushes. He decides to replant all the rose bushes. Each rose bush costs 150. He also needs to pay a gardener 30 an hour, 5 hours each day for 4 days. The final expense is 100 cubic feet of soil sold for 5 per cubic foot. How much did the entire gardening project cost?
answer:The cost to replant all 20 rose bushes is 20 * 150 = 3000. The gardener works 5 hours/day * 4 days = 20 hours in total. So the cost to pay the gardener is 20 hours * 30/hour = 600. The cost of the soil is 100 cubic feet * 5/cubic foot = 500. The total cost of the gardening project is 3000 + 600 + 500 = 4100. 4100 The answer is: 4100