# Three consecutive EVEN integers add up to 30. What are the numbers?

May 27, 2016

$\left\{8 , 10 , 12\right\}$

#### Explanation:

Let $n$ be the least of the three integers. Then the next two will be $n + 2$ and $n + 4$ (the next two even integers). As their sum is $30$, we have

$n + \left(n + 2\right) + \left(n + 4\right) = 30$

$\implies 3 n + 6 = 30$

$\implies 3 n = 24$

$\implies n = 8$

Plugging that back in, that gives us the three integers as

$\left\{n , n + 2 , n + 4\right\} = \left\{8 , 10 , 12\right\}$