# The sum of three consecutive even integers is 228, how do you find the integers?

Jan 26, 2016

$74$, $76$ and $78$

#### Explanation:

Let the first of your integers be $x$.

As you are only looking at even integers, the next consecutive even integer would be $x + 2$ and the consecutive even integer after that would be $x + 4$.

You know that their sum is $228$, so you have

$x + \left(x + 2\right) + \left(x + 4\right) = 228$

$\iff \textcolor{w h i t e}{\times x} x + x + 2 + x + 4 = 228$

$\iff \textcolor{w h i t e}{\times \times \times \times \times x} 3 x + 6 = 228$

Subtract $6$ from both sides of the equation:

$\iff 3 x = 222$

Divide by $3$ on both sides of the equation:

$\iff x = 74$

Thus, your consecutive even integers are $74$, $76$ and $78$.