# 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?

Dec 24, 2016

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

#### 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($f$); $3 n = f$.

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

$3 n + n = 2000$.

$4 n = 2000$

$n = 2000 \div 4$

$n = 500$.

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

$3 \left(500\right) = f$

$1500 = f$.

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