Question

A library contains 2000 books. There are 3 times as many non-fiction as fiction books. How do you write and solve a system of equations to determine the number fiction books and non fiction books?

Answer 1

`n+f=2000`
`3n=f`
`n=500`, `f=1500`

Explanation:

We begin by saying that fiction(`f`) books plus non-fiction(`n`) books equals `2000` books, or `f+n=2000`. Next, we can see that there are three times as many non-fiction(`n`) books as fiction(`f`); `3n=f`.

Now we just use substitution to solve. If `f` equals `3n`, then we just substitute one for the other, like so :

`3n+n=2000`.

`4n=2000`

`n = 2000 -: 4`

`n=500`.

Now we plug `500` in for `n`, and we get

`3(500)=f`

`1500=f`.

To double check our work, `n+f` should equal `2000`. `500+1500=2000`, which is true. Good job!