Question

How do you find three consecutive even integers whose sum is 244?

Answer 1

There are no three consecutive even integers whose sum is 244.

Answer 2

To attempt to find three such integers, you could solve `244 = n+(n+2)+(n+4)` and find that the resulting `n` isn't an integer. So there are no such three consecutive even integers.

Explanation:

If there are three such integers then they are of the form `n`, `n+2` and `n+4`.

Then we have:

`244 = n + (n+2) + (n+4) = 3n+6`

Subtract `6` from both sides to get:

`238 = 3n`

Divide both sides by `3` to get:

`n = 79.dot(3)dot(3)`

which is not an integer, let alone an even one.

So there is no solution.