Question

The product of two consecutive positive integers is 19 more than their sum. Find the integers.

Answer 1

The crucial part of the wording of the problem tells us that the two integers are consecutive. So, let's call the first term x. Then the other term must be x + 1 since it comes right after it and is an integer. Now we can solve:

x(x + 1) = x + (x + 1) + 19

x^2 + x = 2x + 20

x^2 - x - 20 = 0

Now we factor:

(x - 5)(x + 4) = 0

This means x either equals 5 or x = -4 to satisfy the above equation. We know that x is positive from the question itself, so x must be 5. The number consecutively after it then must be 6.