MIT

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question:Find the value of x such that sqrt{1 - 3x} = 7.

answer:First, we square both sides to eliminate the square root: 1 - 3x = 49. Then, we solve for x: -3x = 48. Finally, we divide by -3 to solve for x: x = boxed{-16}.The answer is: -16

question:The bakery made 95 muffins. They will be packed in boxes with 5 muffins in each box. If there are only x available boxes, They still need to pack 9 boxes to pack all the muffins. What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents the number of available boxes to pack the muffins. Let's break down the information given: Total number of muffins: 95 Number of muffins per box: 5 Number of boxes still needed: 9 We can set up the equation as follows: Total number of muffins / Number of muffins per box - Number of boxes still needed = Number of available boxes 95 / 5 - 9 = x Let's simplify and solve for x: 19 - 9 = x 10 = x The value of x is 10. 10 The answer is: 10

question:What is the value of (x - y)(x + y) if x = 10 and y = X? If we know the answer to the above question is -125, what is the value of unknown variable X?

answer:We are given that x - y = 10 and x + y = X. To find the value of (x - y)(x + y), we can substitute the given values of x and y into the expression. (x - y)(x + y) = (10 - X)(10 + X) We are given that the value of (x - y)(x + y) is -125, so we can write: -125 = (10 - X)(10 + X) Now, we can solve for X. Expanding the expression on the right side of the equation, we get: -125 = 100 - X^2 Subtracting 100 from both sides of the equation, we find: -225 = -X^2 Dividing both sides of the equation by -1, we get: 225 = X^2 Taking the square root of both sides of the equation, we find: X = ±15 Since we are looking for the value of X and not x or y, we can ignore the negative solution. Therefore, the value of X is 15. The answer is: 15

question:Dolly wants to ride the Ferris wheel twice, the roller coaster three times, and the log ride seven times. The Ferris wheel costs 2 tickets, the roller coaster costs 5 tickets and the log ride costs 1 ticket. Dolly has x tickets. How many more tickets should Dolly buy? If we know the answer to the above question is 6, what is the value of unknown variable x?

answer:Dolly wants to ride the Ferris wheel twice, which costs 2 tickets per ride, so she needs a total of 2 * 2 = 4 tickets for the Ferris wheel. She wants to ride the roller coaster three times, which costs 5 tickets per ride, so she needs a total of 5 * 3 = 15 tickets for the roller coaster. She wants to ride the log ride seven times, which costs 1 ticket per ride, so she needs a total of 1 * 7 = 7 tickets for the log ride. The total number of tickets Dolly needs is the sum of the tickets for each ride: 4 + 15 + 7 = 26 tickets. We are given that Dolly has x tickets, so the number of tickets she needs to buy is 26 - x. We are also given that she needs to buy 6 more tickets, so we can write: 26 - x = 6. Solving for x, we get: x = 20. The value of x is 20. 20 The answer is: 20