Question

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

Answer 1

`27+28+29 =84`

Explanation:

As the integers are consecutive we could let them be:

`x, x+1 and x+2`

Their sum is `84`

`x+x+1+x+2 = 84`

`3x +3=84`

`3x = 81`

`x = 27`

This is the smallest of the integers which are:

`27, 28 ,29`

Answer 2

`27,28 " 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+(n+1)+(n+2) = 84`

Collect like terms:

`3n+3 = 84`

`=> 3n = 81`

`=> n = 27`

Hence numbers are `n, n+1 , n+2 -> 27, 28 " and " 29`