What are two consecutive even integers such that their sum is equal difference of three times the larger and two times the smaller?

Dec 31, 2017

$4 \mathmr{and} 6$

Explanation:

Let $x =$ the smaller of the consecutive even integers. That means the larger of the two consecutive even integers is$x + 2$ (because even numbers are 2 values apart).

The sum of these two numbers is $x + x + 2.$

The difference of three times the larger number and two times the smaller is $3 \left(x + 2\right) - 2 \left(x\right)$.

Setting the two expressions equal to each other:
$x + x + 2 = 3 \left(x + 2\right) - 2 \left(x\right)$

Simplify and solve:
$2 x + 2 = 3 x + 6 - 2 x$
$2 x + 2 = x + 6$
$x = 4$

So the smaller integer is $4$ and the larger is $6.$