# Find out how many fiction and science books are in the bookstore.

In a bookstore, the number of science books with the number of fiction books stands at 2: 5. There are 150 more fiction books. Find out how many fiction and science books are in the bookstore. There are also 150 science and 500 fiction books in the library. Find out what percent of library books now comprise science books.

• What have you tried? Mar 17, 2020 at 11:43
• What are your thoughts? The usual idea is to assign variables to the various unknowns and then to write out the given information in terms of those variables.
– lulu
Mar 17, 2020 at 11:43

1) Let $$s$$ and $$f$$ be the numbers of science and fiction books respectively. You are given $$s/f = 2/5 \\$$

and $$f = s + 150$$

Therefore $$s/(s + 150) = 2/5 \implies 5s = 2s + 300 \implies 3s = 300 \implies s = 100$$ science books. The number of fiction books is left as an exercise.

2) The second question can be rephrased as "what percent of $$(500+150)$$ library books consist of the $$150$$ science books?". How would you proceed on this one?

The ratio of science books to fiction books is $$2:5$$. It was mentioned that there are $$150$$ more fiction books.

$$5 - 2 = 3$$

$$150 / 3 = 50$$

With this we have found the common ratio $$= 50$$.

$$2 * 50 = 100$$

$$5 * 50 = 250$$

$$250$$ minus $$100$$ is $$150$$, thus confirming the solution. My comprehension on the second part of the question is a little bit fuzzy. Can you elaborate?