The sum of three consecutive odd integers is -51, how do you find the numbers?

What I like to do with these problems is take the number and divide by the number of values we're looking fr, int his case, `3`

so `-51/3 = -17`

Now we find two values that are equally distant from `-17`. They need to be odd numbers and consecutive. The two that follow that pattern are `-19` and `-15`

Let's see if this works:

`-19 + -17 + -15 = -51`

We were right!

First, let's call the smallest number: `n`

Then, the next two consecutive odd numbers would be:

`n + 2` and `n + 4`

We know the sum of these is `-51` so we can write this equation and solve for `n`:

`n + (n + 2) + (n + 4) = -51`

`n + n + 2 + n + 4 = -51`

`n + n + n + 2 + 4 = -51`

`1n + 1n + 1n + 2 + 4 = -51`

`(1 + 1 + 1)n + (2 + 4) = -51`

`3n + 6 = -51`

`3n + 6 - color(red)(6) = -51 - color(red)(6)`

`3n + 0 = -57`

`3n = -57`

`(3n)/color(red)(3) = -57/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = -19`

`n = -19`

Therefore:

• `n + 2 = -19 + 2 = -17`

• `n + 4 = -19 + 4 = -15`

The three consecutive odd integers would be: -19, -17 and -15

`-19 + -17 + -15 => -19 - 17 - 15 => -36 - 15 => -51`