Question #959a1

Oct 16, 2016

$- 40 , - 38 , - 36$

Explanation:

Let $2 n$ represent the least of the even integers. Then, as the integers are consecutive even integers, we have the next two as $2 \left(n + 1\right)$ and $2 \left(n + 2\right)$. Their sum is $- 114$, giving us the equation

$2 n + 2 \left(n + 1\right) + 2 \left(n + 2\right) = - 114$

$\implies 2 n + \left(2 n + 2\right) + \left(2 n + 4\right) = - 114$

$\implies 6 n + 6 = - 114$

$\implies 6 n = - 114 - 6 = - 120$

$\implies n = - \frac{120}{6} = - 20$

$\implies 2 n = - 40 , 2 \left(n + 1\right) = - 38 , 2 \left(n + 2\right) = - 36$

If we check, we find that their sum is $- 114$ as desired.

Thus, our three consecutive even integers are $- 40 , - 38 , - 36$.