Question

The sum of two consecutive integers is −225. Find the two integers

Answer 1

Since the two integers are consecutive, we can let the first be x and the second be x+1.  Then [x] + [x+1] = -225.  Simplifying, 2x + 1 = -225, or
2x = -226.  Thus, x = -113 and x+1 = -113+1 + -112.

The two consecutive integers are -112 and -113.  Adding these together results in -225, as we had hoped.