# How do you find three consecutive even integers whose sum is 16 more than two times the middle integer?

Oct 24, 2016

The three consecutive even integers are $14$, $16$ and $18$.

#### Explanation:

We shall consider the three consecutive even integers as $x$, $x + 2$ and $x + 4$.

From the details we know that the sum of all three is $16$ more than the twice the middle integer.: Expressing this in an equation:

$x + \left(x + 2\right) + \left(x + 4\right) = 2 \left(x + 2\right) + 16$

Opening the brackets and simplifying:

$x + x + 2 + x + 4 = 2 x + 4 + 16$

$3 x + 6 = 2 x + 20$

Shifting terms and simplifying:

$3 x - 2 x = 20 - 6$

$x = 14$

$\therefore x = 14 , x + 2 = 16 , x + 4 = 18$