# The sum of 5 consecutive integers is 1,000. What are the numbers?

Jan 7, 2017

The numbers are: 198, 199, 200, 201 and 202

#### Explanation:

If we let the smallest of the five consecutive integers be $x$,

then the other 4 consecutive integers, by definition of "consecutive" would be:

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

These five integers equal 1,000 so we can write:

$x + x + 1 + x + 2 + x + 3 + x + 4 = 1000$

We can now solve for $x$:

$5 x + 10 = 1000$

$5 x + 10 - \textcolor{red}{10} = 1000 - \textcolor{red}{10}$

$5 x + 0 = 990$

$5 x = 990$

$\frac{5 x}{\textcolor{red}{5}} = \frac{990}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = 198$

$x = 198$

Then:

$x + 1 = 199$

$x + 2 = 200$

$x + 3 = 201$

$x + 4 = 202$