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question:Daniel has a collection of 346 video games. 80 of them, Daniel bought for 12 each. Of the rest, 50% were bought for 7. All others had a price of x each. How much did Daniel spend on all the games in his collection? If we know the answer to the above question is 2290, what is the value of unknown variable x?
answer:Daniel bought 80 video games for 12 each, which means he spent 80 * 12 = 960 on these games. The rest of the games, which is 346 - 80 = 266 games, were bought for different prices. 50% of these games were bought for 7 each, which means there are (50/100) * 266 = 133 games bought for 7 each. The remaining number of games, which is 266 - 133 = 133 games, were bought for x each. The total amount spent on these games is the sum of the amount spent on the 7 games and the amount spent on the x games: 133 * 7 + 133 * x = 931 + 133x. The total amount spent on all the games is the sum of the amount spent on the 12 games and the amount spent on the 7 and x games: 960 + (931 + 133x). We are given that the total amount spent is 2290, so we can write: 960 + (931 + 133x) = 2290. Simplifying the left side, we get: 1891 + 133x = 2290. Subtracting 1891 from both sides, we get: 133x = 399. Dividing both sides by 133, we get: x = 3. The value of x is 3. 3 The answer is: 3
question:John decides to go back to school to get his PhD. He first takes 1 year of courses to get acclimated back to school life before starting his PhD. After that, he spends 2 years learning the basics of his field. He then starts research, and he spends 75% more time on research than he did learning the basics. He then spends half as long on writing his dissertation as his acclimation period. How long did it take him to do everything?
answer:John spends 1 year on courses to get acclimated to school life. He then spends 2 years learning the basics of his field. His research takes 75% more time than learning the basics, so it takes 2 years * 1.75 = 3.5 years. Writing his dissertation takes half as long as his acclimation period, so it takes 1 year / 2 = 0.5 years. To find the total time, we add up all the time periods: 1 year + 2 years + 3.5 years + 0.5 years = 7 years. So, it takes John 7 years to do everything. 7 The answer is: 7
question:Jim has a pail with rocks in it. The average weight of a rock is 1.5 pounds. A local rock collector agrees to pay him x for every pound of rocks. If he makes 60 off the sale, There were 10 rocks in the bucket. What is the value of unknown variable x? What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the amount Jim will be paid for every pound of rocks. Let's break down the information given: Average weight of a rock: 1.5 pounds Number of rocks: 10 Total amount made from the sale: 60 We can set up the equation as follows: Total weight of rocks * Amount paid per pound = Total amount made from the sale 1.5 pounds/rock * 10 rocks * x = 60 Let's simplify and solve for x: 15x = 60 To isolate x, we divide both sides of the equation by 15: 15x / 15 = 60 / 15 x = 4 The value of x is 4. 4 The answer is: 4
question:A board game spinner is divided into three regions labeled A, B and C. The probability of the arrow stopping on region A is frac{1}{2} and on region B is frac{1}{5}. What is the probability of the arrow stopping on region C? Express your answer as a common fraction.
answer:The sum of the probabilities of the arrow stopping on each region must equal 1. Let P(A), P(B), and P(C) be the probabilities of the arrow stopping on regions A, B, and C, respectively. We are given that P(A) = frac{1}{2} and P(B) = frac{1}{5}. Since the sum of the probabilities must equal 1, we have P(A) + P(B) + P(C) = 1. Substituting the given values, we have frac{1}{2} + frac{1}{5} + P(C) = 1. Combining the fractions on the left side, we have frac{5}{10} + frac{2}{10} + P(C) = 1. Simplifying, we have frac{7}{10} + P(C) = 1. Subtracting frac{7}{10} from both sides, we have P(C) = 1 - frac{7}{10} = boxed{frac{3}{10}}. The answer is: frac{3}{10}