Question

Find three positive consecutive integers such that the product of the smallest and the largest is 27 more than three times the median integer.

Answer 1

Let the 3 consecutive positive integers be x, x+1, x+2. The product of the smallest and largest: x(x+2), is 27 more than 3 times the median integer, the one in the middle, which is x+1.
The equation will be:
x(x+2) = 27+3(x+1)
x^2 + 2x = 3x + 30
x^2 - x - 30 = 0
(x - 6)(x + 5) = 0
x = 6 (we don't consider x = -5 since the integers must be positive)
x+1 = 7
x+2 = 8
So the consecutive integers are 6, 7, 8.