Appearance
question:Compute -8cdot 4-(-6cdot -3)+(-10cdot -5).
answer:We start by multiplying -8 and 4, which gives us -32. Next, we multiply -6 and -3, which gives us 18. Finally, we multiply -10 and -5, which gives us 50. Putting it all together, we have -32 - 18 + 50. Simplifying further, we have -32 + 50 - 18. Combining like terms, we get boxed{0}. The answer is: 0
question:Find the only positive real number x for which displaystyle frac{x-4}{9} = frac{4}{x-9}.
answer:Cross-multiplying, we get (x-4)(x-9) = 36. Expanding, we have x^2 - 13x + 36 = 36. Subtracting 36 from both sides, we get x^2 - 13x = 0. Factoring out x, we have x(x-13) = 0. So the solutions are x=0 and x=13, but since we are looking for a positive real number, the only solution is x=boxed{13}. The answer is: 13
question:A whole number, N, is chosen so that frac{N}{3} is strictly between 7.5 and 8. What is the value of N ?
answer:We want frac{N}{3} to be between 7.5 and 8. Multiplying both sides of the inequality by 3, we get N between 7.5times 3=22.5 and 8times 3=24. The only whole number in this range is boxed{23}. The answer is: 23
question:Karen is constantly trying to stop the raccoons from getting in her trash. The first lock she tries stalls them for 5 minutes. The next lock stalls them for 3 minutes less than three times as long as the first lock. When Karen tries both locks at once, it stalled the raccoons for five times as long as the second lock alone. How long is that?
answer:The second lock stalls the raccoons for 3 minutes less than three times as long as the first lock, so it stalls them for 3*5-3 = 12 minutes. When Karen tries both locks at once, it stalls the raccoons for five times as long as the second lock alone, so it stalls them for 5*12 = 60 minutes. 60 The answer is: 60