# The sum of three consecutive integers is 264. What are the three integers?

Feb 10, 2016

$87 , 88 , 89$

#### Explanation:

Let the middle integer be $n$.
Then the three consecutive integers are: $n - 1 , n , n + 1$
and there sum is $3 n$

We are told
$\textcolor{w h i t e}{\text{XXX}} 3 n = 264$
Dividing both sides by $3$, we find
$\textcolor{w h i t e}{\text{XXX}} n = 88$

So the three numbers are $\left(n - 1 , n , n + 1\right) = \left(87 , 88 , 89\right)$

Feb 10, 2016

$87 , 88 , 89$

#### Explanation:

Let the first number be $x$

Then, second number and third number$= x + 1 , x + 2$

Now given is

$x + \left(x + 1\right) + \left(x + 2\right) = 264$

$\implies x + x + 1 + x + 2 = 264$

$\implies 3 x + 3 = 264$

$\implies 3 x = 261$

$\implies x = \frac{261}{3} = 87$

Then the next two integers are $x + 1 = 88 , x + 2 = 89$