Question

What are three consecutive integers whose sum is 51?

Answer 1

The middle one must be the average.

Explanation:

`51div3=17`

So the numbers are `16,17,18`

Note:
This only works with an odd number of integers with constant increments. In other cases you'll have to resort to `x` equations,
in this case `x+(x+1)+(x+2)=51->x=16`

Answer 2

See a solution process below:

Explanation:

Let's call the first integer: `n`

Then, the next two consecutive integers would be:

`n + 1` and `n + 2`

Because their sum is `51` we can write and solve the following equation for `n`:

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

`n + n + 1 + n + 2 = 51`

`n + n + n + 1 + 2 = 51`

`1n + 1n + 1n + 1 + 2 = 51`

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

`3n + 3 = 51`

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

`3n + 0 = 48`

`3n = 48`

`(3n)/color(red)(3) = 48/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 16`

`n = 16`

Therefore:

`n + 1 = 16 + 1 = 17`

`n + 2 = 16 + 2 = 18`

The three consecutive integers which sum to 51 are 16, 17 and 18