# The sum of two consecutive even integers is 26. What are the numbers?

Aug 5, 2016

12 and 14

#### Explanation:

Any even integer can be expressed in the form $2 k$ for $k \in \mathbb{Z}$.

Two consecutive even numbers will thus be $2 \left(k\right) \mathmr{and} 2 \left(k + 1\right)$

$2 \left(k\right) + 2 \left(k + 1\right) = 26$

$4 k + 2 = 26$

$4 k = 24$

$k = 6$

$\implies$ numbers are $12 \mathmr{and} 14$