# The sum of two consecutive even integers is 250. What are the numbers?

Jul 12, 2016

$124 \mathmr{and} 126$

#### Explanation:

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

The first number will be $2 k$ and the second $2 \left(k + 1\right)$.

$2 k + 2 \left(k + 1\right) = 250$

$4 k + 2 = 250$

$k = \frac{250 - 2}{4} = 62$

Numbers are $2 \cdot 62 = 124 \mathmr{and} 2 \cdot 63 = 126$