Question

Five consecutive integers add up to 85. What are the numbers?

Answer 1

The five consecutive integers are `15, 16, 17, 18, 19`

Explanation:

To identify five consecutive integers we begin by giving them each a variable expression

`1st = x`
`2nd = x+ 1`
`3rd=x+2`
`4th = x+3`
`5th = x+4`

Now we set these equal to a sum of 85

`x + x + 1 + x + 2 + x + 3 + x + 4 = 85`

`5x + 10 = 85`

`5x cancel(+ 10) cancel(- 10)= 85 - 10`

`5x = 75`

`(cancel5x)/cancel5 = 75/5`

`x = 15`

`1st = x = 15`
`2nd = x+ 1=16`
`3rd=x+2=17`
`4th = x+3=18`
`5th = x+4=19`

Answer 2

`15, 16, 17, 18, 19`

Explanation:

If the middle integer is `n`, then we are given:

`85 = (n-2)+(n-1)+n+(n+1)+(n+2) = 5n`

Divide both ends by `5` and transpose to find:

`n = 17`

So the five integers are:

`15, 16, 17, 18, 19`