Question

The sum of three consecutive integers is 15. What are the integers?

Answer 1

`4,5,6`

Explanation:

When solving algebraic problems, the first thing we have to do is define a variable for stuff that we don't know. In this problem, we don't know any of the integers, so we assign a variable to them.

Let's have the first integer be `n`. The second integer, since it is right after the first, will be `n+1`. The third integer, since it is right after the second, will be `(n+1)+1=n+2`.

The illustrate this concept, consider the integers `1`, `2`, and `3`. `2` is one more than `1`, or in other words, `2=1+1`. Ditto for `3`, except `3` is two more than `1`, so `3=1+2`. Since the integers are consecutive, each is one more than the last.

We're told that the sum of our three integers is `15`. Therefore,
`n+(n+1)+(n+2)=15`

Solving this equation is pretty straightforward:
`3n+3=15`
`3n=12`
`n=4`

That means our first integer is `4`. Our second integer is `4+1`, or `5`, and our third integer is `5+1`, or `6`. Our answer is confirmed because `4+5+6=15`.