# How do you find three consecutive odd integers such that the sum of the first, two times the second and three times the third is 34?

Jan 23, 2016

Set up an equation to find the integers to be
$3 , 5 , 7$

#### Explanation:

Let $n$ be the least of the integers. Then the second is $n + 2$ and the third is $n + 4$, so we have

$n + 2 \left(n + 2\right) + 3 \left(n + 4\right) = 34$

$\implies n + 2 n + 4 + 3 n + 12 = 34$

$\implies 6 n + 16 = 34$

$\implies 6 n = 18$

$\implies n = 3$

Thus the integers are $3 , 5 , 7$