# The sum of three consecutive even integers is 42, what are the integers?

Oct 16, 2015

$12$, $14$, and $16$

#### Explanation:

You know that thee consecutive even integers add up to give $42$.

If you take $2 x$ to be the first even number of the series, you can say that

$2 x + 2 \to$ the second number of the series

$\left(2 x + 2\right) + 2 = 2 x + 4 \to$ the third number of the series

This means that you have

${\overbrace{2 x}}^{\textcolor{b l u e}{\text{first even no.")) + overbrace((2x + 2))^(color(red)("second even no.")) + overbrace((2x + 4))^(color(purple)("third even no.}}} = 42$

This is equivalent to

$6 x + 6 = 42$

$6 x = 36 \implies x = \frac{36}{6} = 6$

The three consecutive even integers that add up to $42$ are

$2 \cdot x = 12$

$2 \cdot x + 2 = 14$

$2 \cdot x + 4 = 16$