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question:Trent caught 180 tadpoles then let x% of them go. He kept 45. 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 percentage of tadpoles that Trent let go. Let's break down the information given: Number of tadpoles caught: 180 Number of tadpoles kept: 45 We can set up the equation as follows: Number of tadpoles kept = (100 - x)% of the number of tadpoles caught 45 = (100 - x)% * 180 Let's simplify and solve for x: 45 = (100 - x)/100 * 180 To eliminate the fraction, we multiply both sides of the equation by 100: 45 * 100 = (100 - x)/100 * 180 * 100 4500 = 18000 - 180x To isolate x, we subtract 18000 from both sides of the equation: 4500 - 18000 = 18000 - 180x - 18000 -13500 = -180x To solve for x, we divide both sides of the equation by -180: -13500 / -180 = -180x / -180 75 = x The value of x is 75. 75 The answer is: 75
question:Liam is teaching art to a group of 10 students. He has 20 art kits that he hands out to the students to share, 1 art kit for 2 students. From those art kits half the students make 3 artworks each and half the students make x artworks each. How many artistic works does the whole class create? If we know the answer to the above question is 35, what is the value of unknown variable x?
answer:We know that Liam has 20 art kits for 10 students, so each art kit is shared between 2 students. Half of the students make 3 artworks each, which means there are 10/2 = 5 students making 3 artworks each. The total number of artworks created by these students is 5 * 3 = 15 artworks. The other half of the students make x artworks each, which means there are 10/2 = 5 students making x artworks each. The total number of artworks created by these students is 5 * x = 5x artworks. The total number of artworks created by the whole class is the sum of the artworks created by the two groups of students: 15 + 5x. We are given that the total number of artworks created is 35, so we can write: 15 + 5x = 35. Solving for x, we get: 5x = 20. Dividing both sides by 5, we get: x = 4. The value of x is 4. 4 The answer is: 4
question:What is the positive integer N for which 22^2 times 55^2 = 10^2 times N^2 ?
answer:We can simplify the equation by taking the square root of both sides: sqrt{22^2 times 55^2} = sqrt{10^2 times N^2}. Simplifying the left side gives 22 times 55 = 10N. Dividing both sides by 10 gives 22 times 55 div 10 = N. Calculating this gives N = boxed{121}.The answer is: 121
question:After Martha went grocery shopping she had x bottles of juice in the refrigerator and 4 bottles in the pantry. During the week Martha bought 5 more bottles of juice. If Martha and her family drank 3 bottles of juice during the week, There are 10 bottles left. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the initial number of bottles of juice Martha had in the refrigerator. Let's break down the information given: Number of bottles of juice Martha had in the refrigerator: x Number of bottles of juice Martha had in the pantry: 4 Number of bottles of juice Martha bought during the week: 5 Number of bottles of juice Martha and her family drank during the week: 3 Number of bottles of juice left: 10 We can set up the equation as follows: Number of bottles of juice in the refrigerator + Number of bottles of juice in the pantry + Number of bottles of juice bought during the week - Number of bottles of juice drank during the week = Number of bottles of juice left x + 4 + 5 - 3 = 10 Let's simplify and solve for x: x + 6 = 10 To isolate x, we subtract 6 from both sides of the equation: x + 6 - 6 = 10 - 6 x = 4 The value of x is 4. 4 The answer is: 4