# How do you find the two numbers if the smaller of 2 consecutive even integers is 5 more than one- half the greater?

Jun 2, 2015

Let the smaller of the two consecutive even integers be $2 x$.
Therefore the larger of the two consecutive even integers is $2 x + 2$.

We are told
$\textcolor{w h i t e}{\text{XXXXX}}$$2 x - 5 = \frac{1}{2} \left(2 x + 2\right)$

Which implies
$\textcolor{w h i t e}{\text{XXXXX}}$$2 x - 5 = x + 1$

$\textcolor{w h i t e}{\text{XXXXX}}$$x = 6$

and the two consecutive even integers ($2 x$ and $2 x + 2$) are
$\textcolor{w h i t e}{\text{XXXXX}}$ 12 and 14.