# Three consecutive integers have a sum of 84, what are the integers?

Apr 12, 2018

$27 + 28 + 29 = 84$

#### Explanation:

As the integers are consecutive we could let them be:

$x , x + 1 \mathmr{and} x + 2$

Their sum is $84$

$x + x + 1 + x + 2 = 84$

$3 x + 3 = 84$

$3 x = 81$

$x = 27$

This is the smallest of the integers which are:

$27 , 28 , 29$

Apr 12, 2018

$27 , 28 \text{ and } 29$

#### Explanation:

Let the first be $n$, and if they are consecutive then the next two numbers are $n + 1$ and $n + 2$

The sum means addition:

$n + \left(n + 1\right) + \left(n + 2\right) = 84$

Collect like terms:

$3 n + 3 = 84$

$\implies 3 n = 81$

$\implies n = 27$

Hence numbers are $n , n + 1 , n + 2 \to 27 , 28 \text{ and } 29$