# If the average of 5 consecutive integers is 12, what is the sum of the least and greatest of the 5 integers?

##### 1 Answer
May 26, 2017

$24$

#### Explanation:

$\text{let the 5 consecutive integers be}$

$n , \textcolor{w h i t e}{x} n + 1 , \textcolor{w h i t e}{x} n + 2 , \textcolor{w h i t e}{x} n + 3 , \textcolor{w h i t e}{x} n + 4$

$\Rightarrow \text{sum of the 5 integers} = 12 \times 5 = 60$

$= n + \left(n + 1\right) + \left(n + 2\right) + \left(n + 3\right) + \left(n + 4\right) = 5 n + 10$

$\Rightarrow 5 n + 10 = 60 \leftarrow \text{ and solving for n}$

$\Rightarrow n = 10$

$\Rightarrow 10 , \textcolor{w h i t e}{x} 11 , \textcolor{w h i t e}{x} 12 , \textcolor{w h i t e}{x} 13 , \textcolor{w h i t e}{x} 14 \leftarrow \textcolor{red}{\text{ are the 5 integers}}$

$\text{sum of least and greatest } = 10 + 14 = 24$