# How do you find three consecutive odd integers whose sum is 13 more than twice the largest of the three?

Jan 24, 2016

Interpret the description in terms of an unknown smallest integer $n$ and solve to find integers:

$15 , 17 , 19$

#### Explanation:

Suppose the three odd integers are $n$, $n + 2$ and $n + 4$

Their sum is:

$n + \left(n + 2\right) + \left(n + 4\right) = 3 n + 6$

$13$ more than twice the largest of the three is:

$2 \left(n + 4\right) + 13 = 2 n + 21$

From what we are told these two are equal:

$3 n + 6 = 2 n + 21$

Subtract $2 n + 6$ from both sides to get:

$n = 15$

So the three integers are:

$15 , 17 , 19$