Question

A self at a bookstore displays 27 books. Of these 27 books, 9 of the books are nonfiction books. The store owner adds 6 new fiction books to the shelf and wants the ratio of fiction books to nonfiction books to remain the same. What is the total number of nonfiction books that the store should display, after the new fiction books are added?

Answer 1

Right now, the ratio of nonfiction to fiction is 9:18.  If this is reduced, it is a ratio of 1:2, so there needs to be twice as many fiction books as nonfiction.

If we add 6 fiction books, we have 24 fiction books.  We can now set up this equation:

$\frac{1}{2} = \frac{x}{24}$

Now we cross multiply

$2x=24$

We can solve for x by dividing both sides by two, so:

x = 12.  There will be 12 nonfiction books.