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?

1 Answer
Dec 24, 2016

Answer:

#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!