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question:f Richard takes 22 minutes to clean his room, Cory takes 3 minutes longer than Richard, and Blake takes 4 minutes less time than Cory, and they have to clean their rooms twice a week, what is the total number of minutes they spend cleaning their rooms each week?
answer:Richard takes 22 minutes to clean his room. Cory takes 3 minutes longer, so he takes 22 + 3 = 25 minutes to clean his room. Blake takes 4 minutes less, so he takes 25 - 4 = 21 minutes to clean his room. They each clean their rooms twice a week, so Richard spends 22 * 2 = 44 minutes cleaning his room each week. Cory spends 25 * 2 = 50 minutes cleaning his room each week. Blake spends 21 * 2 = 42 minutes cleaning his room each week. The total number of minutes they spend cleaning their rooms each week is 44 + 50 + 42 = 136 minutes. 136 The answer is: 136
question:The sum of three consecutive one-digit, positive, odd integers is one-seventh of the product of the same three integers. What is the middle integer when the three integers are listed in ascending order?
answer:Let the three integers be n, n + 2, and n + 4. Then n + (n + 2) + (n + 4) = frac{1}{7} cdot n(n + 2)(n + 4). Simplifying the left side gives 3n + 6 = frac{1}{7} cdot n(n + 2)(n + 4). Multiplying both sides by 7 gives 21n + 42 = n(n + 2)(n + 4). Expanding and rearranging gives n^3 + 6n^2 + 8n - 42 = 0. Factoring this equation gives (n - 3)(n^2 + 9n + 14) = 0. Thus, n = 3 or n^2 + 9n + 14 = 0. The quadratic equation n^2 + 9n + 14 = 0 does not have real solutions, so the only possible value for n is 3. Therefore, the middle integer is n + 2 = 3 + 2 = boxed{5}. The answer is: 5
question:Let astar b = ab+2b-a. If 5star x = 37, find the value of x.
answer:We substitute 5 for a and x for b in the expression ab+2b-a to get 5x+2x-5=37. Combining like terms, we have 7x-5=37. Adding 5 to both sides gives 7x=42, and dividing both sides by 7 gives x=boxed{6}. The answer is: 6
question:Quinten sees three buildings downtown and decides to estimate their heights. He knows from a book on local buildings that the one in the middle is 100 feet tall. The one on the left looks like it is 80% of the height of the middle one. The one on the right looks 20 feet shorter than if the building on the left and middle were stacked on top of each other. How tall does Quinten estimate their total height to be?
answer:The building on the left is estimated to be 80% of the height of the middle building, so it is 80/100 * 100 = 80 feet tall. If the building on the left and middle were stacked on top of each other, their total height would be 100 + 80 = 180 feet. The building on the right is estimated to be 20 feet shorter than if the building on the left and middle were stacked on top of each other, so it is 180 - 20 = 160 feet tall. The total estimated height of the three buildings is 100 + 80 + 160 = 340 feet. 340 The answer is: 340