# How do you find four consecutive integers whose sum is 114?

Oct 19, 2016

The four numbers are $27 , 28 , 29 , \mathmr{and} 30$

#### Explanation:

Let the smallest number be $n$.
Then the four numbers are $n , n + 1 , n + 2 , \mathmr{and} n + 3$
and their sum is
$\textcolor{w h i t e}{\text{XXX}} n + \left(n + 1\right) + \left(n + 2\right) + \left(n + 3\right) = 4 n + 6$

We are told that this sum is equal to $114$
So
$\textcolor{w h i t e}{\text{XXX}} 4 n + 6 = 114$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 n = 108$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow n = 27$