ANSWER
There are 16 fiction books
EXPLANATION
Let the number of nonfiction books be
[tex]n[/tex]
Then the number of fiction books is
[tex]f=\frac{2n}{5} [/tex]
If there are 56 books in the library, then
[tex]n + f= 56[/tex]
This implies that,
[tex]n + \frac{2n}{5} = 56[/tex]
Multiply through by 5 to get,
[tex]5n + 2n = 280[/tex]
[tex]7n= 280[/tex]
Divide through by 7 to get,
[tex]n = \frac{280}{7} [/tex]
[tex]n= 40[/tex]
Therefore the number of fiction books
[tex] f=\frac{2\times40}{5}=16 [/tex]
Or
[tex]f=56 - 40 = 16[/tex]
