Question

On a bookshelf, all books are sorted by

whether they are fiction or non-fiction and
whether they are paperback or hardback.
The ratio of fiction books to non-fiction books
is 6 : 1.
The ratio of paperback fiction books to
hardback fiction books is 11 : 4.
The ratio of paperback non-fiction books to
hardback non-fiction books is 3 : 2.
Work out what fraction of the books are
hardback.
Give your answer in its simplest form.

Answer 1

To find the fraction of hardback books, we need to calculate the total number of hardback books and divide it by the total number of books.

Step-by-step explanation:

To find the fraction of hardback books, we need to calculate the total number of hardback books and divide it by the total number of books. First, let's determine the number of fiction and non-fiction books. Let's assume there are 6x fiction books and x non-fiction books. So, the total number of books is 7x (6x fiction + x non-fiction).

Next, let's calculate the number of paperback and hardback fiction books. The ratio of paperback fiction books to hardback fiction books is given as 11:4, which means there are 11y paperback fiction books and 4y hardback fiction books. Similarly, there are 3z paperback non-fiction books and 2z hardback non-fiction books.

Since the total number of books is 7x, we can write the equation as:
7x = 11y + 4y + 3z + 2z

To get the fraction of hardback books, we need to find the ratio of hardback books to the total number of books:
Hardback books / Total books = (4y + 2z) / 7x

To simplify the expression, we can find the common factors in the numerator and denominator. Then, divide each term by the common factors and simplify if possible.