# The sum of three consecutive odd integers is 351, how do you find the three integers?

May 4, 2018

I got: $115 , 117 \mathmr{and} 119$

#### Explanation:

let us call our integers:
$2 n + 1$
$2 n + 3$
$2 n + 5$
we get:
$2 n + 1 + 2 n + 3 + 2 n + 5 = 351$
rearrange:
$6 n = 351 - 9$
so that:
$n = \frac{342}{6} = 57$
our integers will then be:
$2 n + 1 = 115$
$2 n + 3 = 117$
$2 n + 5 = 119$

May 4, 2018

115, 117 & 119

#### Explanation:

We can represent the three integers by using the variable $x$

1st odd integer $= x$
2nd odd integer $= x + 2$ consecutive integers would be $x + 1$
3rd odd integer $= x + 4$

The sum means we need to add

$x + x + 2 + x + 4 = 351$

Combine like terms
$3 x + 6 = 351$

Use additive inverse to isolate the variable term
$3 x \cancel{+ 6} \cancel{- 6} = 351 - 6$

$3 x = 345$

Use the multiplicative inverse to isolate the variable
$\frac{\cancel{3} x}{\cancel{3}} = \frac{345}{3}$

$x = 115$
$x + 2 = 117$
$x + 4 = 119$