# How do you find three consecutive odd integers with the sum of 273?

Jan 16, 2017

See entire solution process below.

#### Explanation:

First, let's name the three consecutive odd integers.

We can call the first integer $i$.

Then, because they are "consecutive odd integers" we need to add $2$ and $4$ to the first integer.

Therefore, the 3 consecutive odd integers are: $i$, $i + 2$ and $i + 4$.

There three sum to 273 so we can write and solve for $i$:

$i + i + 2 + i + 4 = 273$

$i + i + i + 2 + 4 = 273$

$3 i + 6 = 273$

$3 i + 6 - \textcolor{red}{6} = 273 - \textcolor{red}{6}$

$3 i + 0 = 267$

$3 i = 267$

$\frac{3 i}{\textcolor{red}{3}} = \frac{267}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} i}{\cancel{\textcolor{red}{3}}} = 89$

$i = 89$

and

$i + 2 = 91$

and

$i + 4 = 93$

The three consecutive odd integers are:

89 + 91 + 93 = 273