# Four consecutive even integers add up to 52. What are the numbers?

Apr 17, 2017

$n = 10 , 12 , 14 , 16$

#### Explanation:

$n + n + 2 + n + 4 + n + 6 = 52$
$4 n + 12 = 52$
$4 n = 40$
$n = 10$

Apr 17, 2017

$10 , 12 , 14 , 16$

#### Explanation:

A generic even integer can be represented by $2 n$ where $n$ itself is also an integer

So then, the four consecutive integers would be:

$2 n , 2 n + 2 , 2 n + 4 , 2 n + 6$

We know that the sum of these integers is $52$ and so;

$2 n + \left(2 n + 2\right) + \left(2 n + 4\right) + \left(2 n + 6\right) = 52$

$\therefore 8 n + 12 = 52$
$\therefore 8 n = 40$
$\therefore n = 5$

And so with this value of n the even consecutive numbers are:

$10 , 12 , 14 , 16$