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question:Carl has a jar full of marbles. He takes out x marbles to play a game with, but he accidentally drops them and 1/2 the marbles get lost. So Carl takes out 10 more marbles. While he is playing his game his mother comes home with another bag of marbles for him, which has 25 marbles in it. If Carl can't find his lost marbles, then how many marbles is he going to put in the jar after he plays his game, From both his original marbles and the new ones, there are 41. 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 marbles Carl initially took out of the jar to play the game. Let's break down the information given: Number of marbles initially taken out: x Number of lost marbles: 1/2 * x Number of additional marbles taken out: 10 Number of marbles in the new bag: 25 Total number of marbles after playing the game: 41 We can set up the equation as follows: Number of marbles initially taken out - Number of lost marbles + Number of additional marbles taken out + Number of marbles in the new bag = Total number of marbles after playing the game x - (1/2 * x) + 10 + 25 = 41 Let's simplify and solve for x: x - (1/2 * x) + 35 = 41 To simplify further, we can multiply 1/2 by x: x - (x/2) + 35 = 41 To simplify even further, we can find the common denominator of 2: 2x/2 - x/2 + 35 = 41 (2x - x)/2 + 35 = 41 x/2 + 35 = 41 To isolate x/2, we subtract 35 from both sides of the equation: x/2 + 35 - 35 = 41 - 35 x/2 = 6 To solve for x, we multiply both sides of the equation by 2: (2*x/2) = 6*2 x = 12 The value of x is 12. 12 The answer is: 12
question:The number 236! ends in how many zeros when expressed as an integer?
answer:A number ends in a zero if it is divisible by 10, which is equal to 2 times 5. Since there are more factors of 2 than 5 in any factorial, we only need to count the number of factors of 5. To count the number of factors of 5 in 236!, we can divide 236 by 5, then divide the quotient by 5 again, and so on, until the quotient is less than 5. Doing this, we get leftlfloor frac{236}{5} rightrfloor + leftlfloor frac{236}{25} rightrfloor + leftlfloor frac{236}{125} rightrfloor = 47 + 9 + 1 = 57. Therefore, 236! ends in boxed{57} zeros. The answer is: 57
question:Lily had 55 in her account. She spent 7 on a shirt. She then went to another shop and spent thrice as much as she spent on a shirt. How much money is left in Lily's account?
answer:Lily had 55 in her account. She spent 7 on a shirt, so she has 55 - 7 = 48 left in her account. She then went to another shop and spent thrice as much as she spent on a shirt, which is 7 x 3 = 21. Therefore, she has 48 - 21 = 27 left in her account. 27 The answer is: 27
question:Terry's daily income is 24, while Jordan's daily income is 30. Working x days a week, how much is the difference between their weekly incomes? If we know the answer to the above question is 42, what is the value of unknown variable x?
answer:Terry's daily income is 24, so his weekly income is 24 * x. Jordan's daily income is 30, so his weekly income is 30 * x. The difference between their weekly incomes is: (30 * x) - (24 * x) = 6 * x. We are given that the difference between their weekly incomes is 42, so we can write: 6 * x = 42. Dividing both sides by 6, we get: x = 7. The value of x is 7. 7 The answer is: 7