Question

The sum of three consecutive odd integers is -87. What are the integers?

Answer 1

`{-31, -29, -27}`

Explanation:

Any odd integer may be expressed as `2n+1` for some integer `n`. As we are looking for three consecutive odd integers, we will represent the least as `2n+1`, and the next two as `2n+3`, and `2n+5`. With that, we have

`(2n+1)+(2n+3)+(2n+5) = -87`

`=> 6n+9 = -87`

`=> 6n = -96`

`=> n = -16`

Then, the three odd integers are

`{2(-16)+1, 2(-16)+3, 2(-16)+5}`

`= {-31, -29, -27}`

Answer 2

`-31, -29, -27`

Explanation:

Alternatively, suppose the second consecutive odd integer is `n`.

Then the first and third are `(n-2)` and `(n+2)`.

So:

`-87 = (n-2)+n+(n+2) = 3n`

Divide both ends by `3` to get:

`-29 = n`

So the three consecutive odd integers are:

`-31, -29, -27`