# What is the greatest of 5 consecutive integers if the sum of these integers equals 185?

Feb 4, 2017

39 is the greatest of the 5 consecutive integers adding to 185.

#### Explanation:

First, let's define the 5 consecutive integers.

We can call the smallest of the 5 consecutive integers $x$.

Then, by definition of "consecutive integers" the remaining 4 would be:

$x + 1$, $x + 2$, $x + 3$ and $x + 4$

The sum of these 5 consecutive integers equals 185 so we can write and solve for $x$:

$x + x + 1 + x + 2 + x + 3 + x + 4 = 185$

$5 x + 10 = 185$

$5 x + 10 - \textcolor{red}{10} = 185 - \textcolor{red}{10}$

$5 x + 0 = 175$

$5 x = 175$

$\frac{5 x}{\textcolor{red}{5}} = \frac{175}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = 35$

$x = 35$

We are looking for the greatest of the 5 consecutive integers or $x + 4 \to 35 + 4 = 39$