The difference between two positive integers is 6 and their product is 112. What is the sum of the integers?
I need to find two positive integers, x and y, such that x - y = 6 and x * y = 112. I could try to factor 112 and look for two factors that differ by 6, but that might take a long time. If I solve for x in terms of y, I get x = y + 6. Then I can substitute this expression into the second equation and get (y + 6) * y = 112. This is a quadratic equation that I can solve by expanding, rearranging, and factoring. I get y^2 + 6y - 112 = 0. I can factor this into (y - 8) * (y + 14) = 0. So y = 8 or y = -14. Since y has to be a positive integer, I can reject the negative solution and conclude that y = 8. Then x = y + 6, so x = 8 + 6 = 14. The sum of the integers is x + y = 14 + 8 = 22.

