# The sum of three consecutive integers is 135. What are the numbers?

Jul 4, 2017

$44 , 45 , 46$

#### Explanation:

$\text{let the first integer be represented by } n$

$\text{then the second integer will be } n + 1$

$\text{and the third integer } n + 2$

$\Rightarrow n + n + 1 + n + 2 = 135 \leftarrow \textcolor{b l u e}{\text{ sum of integers}}$

$\Rightarrow 3 n + 3 = 135 \leftarrow \textcolor{b l u e}{\text{ simplifying left side}}$

$\text{subtract 3 from both sides}$

$3 n \cancel{+ 3} \cancel{- 3} = 135 - 3$

$\Rightarrow 3 n = 132$

$\text{divide both sides by 3}$

$\frac{\cancel{3} n}{\cancel{3}} = \frac{132}{3}$

$\Rightarrow n = 44$

$\Rightarrow n + 1 = 44 + 1 = 45$

$\Rightarrow n + 2 = 44 + 2 = 46$

$\text{the three consecutive integers are } 44 , 45 , 46$

$\textcolor{b l u e}{\text{As a check}}$

$44 + 45 + 46 = 135 \rightarrow \text{ True}$