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question:Gary is buying chlorine for his rectangular pool, which is 10 feet long, 8 feet wide, and x feet deep. Gary needs to buy one quart of chlorine for every 120 cubic feet of water in his pool. If chlorine costs 3 a quart, how much does Gary spend on chlorine? If we know the answer to the above question is 12, what is the value of unknown variable x?

answer:The volume of a rectangular pool is calculated by multiplying its length, width, and depth: volume = length * width * depth = 10 * 8 * x = 80x cubic feet. Gary needs one quart of chlorine for every 120 cubic feet of water, so he needs (80x) / 120 = (4x) / 6 = (2x) / 3 quarts of chlorine. Chlorine costs 3 per quart, so Gary spends (2x/3) * 3 = (2/3) * 3x = 2x on chlorine. We are given that Gary spends 12 on chlorine, so we can write: 2x = 12. Dividing both sides by 2, we get: x = 6. The value of x is 6. 6 The answer is: 6

question:Amerigo Vespucci has a map of America drawn on the complex plane. The map does not distort distances. Los Angeles corresponds to 0 on this complex plane, and Boston corresponds to 2600i. Meanwhile, Knoxville corresponds to the point 780+1040i. With these city-point correspondences, how far is it from Knoxville to Los Angeles on this complex plane?

answer:We can find the distance between Knoxville and Los Angeles by subtracting their complex coordinates. The complex coordinate for Los Angeles is 0, and the complex coordinate for Knoxville is 780+1040i. So, the distance between Knoxville and Los Angeles is given by begin{align*} |780+1040i-0| &= |780+1040i| &= sqrt{780^2 + 1040^2} &= sqrt{608400 + 1081600} &= sqrt{1690000} &= boxed{1300}. end{align*} The answer is: 1300

question:Karen bakes 50 chocolate chip cookies. She keeps 10 for herself, and she gives 8 to her grandparents. If Karen wants to give everyone in her class cookies, and there are 16 people in her class, how many cookies will each person receive?

answer:Karen bakes 50 cookies and keeps 10 for herself, so she has 50 - 10 = 40 cookies left. She gives 8 cookies to her grandparents, so she has 40 - 8 = 32 cookies left. Karen wants to give cookies to 16 people in her class, so each person will receive 32 / 16 = 2 cookies. Each person in Karen's class will receive 2 cookies. 2 The answer is: 2

question:After spending 2 on bread, 3 on butter, and an amount on juice that is twice the price of the bread, Paul had 15 for his shopping. What is the amount of money that Paul has left after his shopping?

answer:Paul spent 2 on bread and 3 on butter, so he spent a total of 2 + 3 = 5 on bread and butter. The price of the juice is twice the price of the bread, so it is 2 * 2 = 4. So, Paul spent a total of 5 + 4 = 9 on bread, butter, and juice. He had 15 for his shopping, so he has 15 - 9 = 6 left after his shopping. 6 The answer is: 6