# The sum of three consecutive odd integers is 99. What are the three numbers?

Jan 21, 2016

I found $31 , 33 , 35$

#### Explanation:

Let us call our odd integers:
$2 n + 1$
$2 n + 3$
$2 n + 5$
and write our condition as:
$\left(2 n + 1\right) + \left(2 n + 3\right) + \left(2 n + 5\right) = 99$ and solve it for $n$:
$6 n + 9 = 99$
$6 n = 90$
$n = \frac{90}{6} = 15$
so our numbers will be:
$2 n + 1 = 31$
$2 n + 3 = 33$
$2 n + 5 = 35$