Answer:
There are 16 fiction books in the library.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of fiction books and y be the number of non fiction books.
Total number of books = 56
Thus, we can write the equation:
[tex]x+y = 56[/tex]
There are [tex]\frac{2}{5}[/tex] as many fiction books as there are nonfiction books.
Thus, we can write the equation:
[tex]x = \dfrac{2}{5}y[/tex]
Solving the two equations by substitution, we get,
[tex]\dfrac{2}{5}y + y = 56\\\\\dfrac{7}{5}y = 56\\\\y = 56\times \dfrac{5}{7}\\\\y = 40[/tex]
Thus, there are 40 non fiction books.
Number of fiction books =
[tex]x = 56 - 40 = 16[/tex]
Thus, there are 16 fiction books in the library.
