Question

One shelf at Cover-to-Cover Bookstore contains copies of several books on the best-seller list. Half of the books on the shelf are copies of the Number 1 best- seller. Of the remainder, 1/4 are copies of the Number 3 book. The rest are copies of the Number 2 book. If there are 5 copies the Number 2 book, how many best sellers are on the shelf?

Answer 1

The number of best sellers on the shelf are 13.333 best sellers

Explanation:

The question is a word problem with the following specifications;

Proportion of the books, B, on the shelf that are number 1 best seller = 1/2 of B

Proportion of the books that are Number 3 book = 1/4 of (1 - 1/2) of B

Proportion of the books that are Number 2 book = 1/2 - 1/4 of (1 - 1/2) of B

Given that there are 5 copies of Number 2 book we have;

1/2 - 1/4 × (1 - 1/2) × B = 3/8 × B = 5

Which gives the number of best sellers on the shelf as B = 40/3 books

If there is a grammatical misunderstanding, we should have;

There appear to be an error in grammar as the statement maybe should have read as follows

Half of the books on he shelf are copes of the Number 1 best seller. The remainder are 1/4 copies of the Number 3 book.....

Which gives;

Proportion of the books that are Number 3 book = 1/4 of B

Proportion of the books that are Number 2 book = (1 - 1/2 - 1/4) of B

Given that there are 5 copies of Number 2 book we have;

(1 - 1/2 - 1/4) × B = 1/4 × B = 5

Which gives the number of best sellers on the shelf as B = 20 books.