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question:There are three dogs in the backyard. They like apples, blueberries, and bonnies. The first dog, which likes apples, eats 3 times as many apples as the number of blueberries eaten by the second dog that likes blueberries. The dog that likes blueberries eats 3/4 times as many blueberries as the number of bonnies eaten by the third dog. If the dog that likes bonnies ate x of them, The total number of fruits eaten by the three dogs is 240. 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 bonnies eaten by the third dog. Let's break down the information given: Number of apples eaten by the first dog: 3 times the number of blueberries eaten by the second dog Number of blueberries eaten by the second dog: 3/4 times the number of bonnies eaten by the third dog Number of bonnies eaten by the third dog: x Total number of fruits eaten by the three dogs: 240 We can set up the equation as follows: Number of apples eaten by the first dog + Number of blueberries eaten by the second dog + Number of bonnies eaten by the third dog = Total number of fruits eaten by the three dogs 3(3/4x) + 3/4x + x = 240 Let's simplify and solve for x: 9/4x + 3/4x + x = 240 Multiplying all terms by 4 to eliminate the fractions: 9x + 3x + 4x = 960 16x = 960 To solve for x, we divide both sides of the equation by 16: x = 960 / 16 x = 60 The value of x is 60. 60 The answer is: 60
question:Rajesh walked 10 kilometers less than 4 times the distance that Hiro walked. Together they walked 25 kilometers. How many kilometers did Rajesh walk?
answer:Let's assume the distance Hiro walked is x kilometers. Rajesh walked 10 kilometers less than 4 times the distance Hiro walked, so Rajesh walked 4x - 10 kilometers. Together they walked 25 kilometers, so we have the equation x + 4x - 10 = 25. Combining like terms, we get 5x - 10 = 25. Adding 10 to both sides, we get 5x = 35. Dividing both sides by 5, we get x = 7. So, Hiro walked 7 kilometers. Substituting this value back into the equation for Rajesh, we get 4(7) - 10 = 28 - 10 = 18. Therefore, Rajesh walked 18 kilometers. 18 The answer is: 18
question:f a triangle is formed by joining wood sticks of lengths 8, 15, and 17 inches, and pieces of the same integral length are cut from each stick, what is the length of the smallest piece that can be cut from each stick so that the remaining pieces can no longer form a triangle?
answer:To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If we cut a piece of length x from each stick, the remaining pieces will have lengths 8-x, 15-x, and 17-x. For these remaining pieces to no longer form a triangle, we must have either (8-x)+(15-x) leq (17-x) or (8-x)+(17-x) leq (15-x) or (15-x)+(17-x) leq (8-x). Simplifying these inequalities gives x geq 6, x geq 2, and x geq 4 respectively. The smallest value of x that satisfies all three inequalities is boxed{6}. The answer is: 6
question:Jose had 400 tabs opened up in his windows browser. After about one hour of browsing, he closed 1/4 of the tabs to allows easy browsing. He read some news from different pages, then closed 2/5 of the remaining tabs. If he closed x% of the remaining tabs after further analyzing some pages, He had 90 windows tabs remaining open. 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 tabs that Jose closed after further analyzing some pages. Let's break down the information given: Initial number of tabs: 400 Number of tabs closed after one hour: 1/4 * 400 = 100 Number of tabs remaining: 400 - 100 = 300 Number of tabs closed after reading news: 2/5 * 300 = 120 Number of tabs remaining after reading news: 300 - 120 = 180 Number of tabs remaining after further analyzing some pages: 90 We can set up the equation as follows: Number of tabs remaining * (1 - x/100) = Number of tabs after further analyzing some pages 180 * (1 - x/100) = 90 Let's simplify and solve for x: 180 - 1.8x = 90 To isolate x, we subtract 180 from both sides of the equation: 180 - 180 - 1.8x = 90 - 180 -1.8x = -90 To solve for x, we divide both sides of the equation by -1.8: x = -90 / -1.8 x = 50 The value of x is 50. 50 The answer is: 50