# The sum of four consecutive even integers is 84, what are the integers?

May 31, 2015

Suppose the integers are $n$, $n + 2$, $n + 4$ and $n + 6$

Then

$84 = n + \left(n + 2\right) + \left(n + 4\right) + \left(n + 6\right) = 4 n + 12$

Subtract $12$ from both ends to get

$72 = 4 n$

Divide both ends by $4$ to get

$n = 18$

So the integers are: $18$, $20$, $22$, $24$