Question

How do you find four consecutive integers whose sum is 114?

Answer 1

The four numbers are `27, 28,29,and 30`

Explanation:

Let the smallest number be `n`.
Then the four numbers are `n, n+1, n+2, and n+3`
and their sum is
`color(white)("XXX")n+(n+1)+(n+2)+(n+3)=4n+6`

We are told that this sum is equal to `114`
So
`color(white)("XXX")4n+6=114`

`color(white)("XXX")rarr 4n=108`

`color(white)("XXX")rarr n=27`