Question

A group of 15 people each bought both a book that cost x dollars and a bookmark that cost $1. A group of 3 people each bought both a book that cost x dollars and a backpack that cost $36. Both groups spent the same amount of money. What is the price of the book?

Answer 1

$1.40

Explanation:

Answer 2

The price of the book is $7.75.

Explanation:

Let's first establish an equation.

If I buy a book costing
`x` dollars and a bookmark costing 1 dollars, I will have spent
`x + 1` dollars. So a group of 15 people doing the same will have spent
`15(x+1) = 15x + 15` dollars.

Analogously, the group of 3 people has spent
`3(x+36) = 3x + 108` dollars.

Since we know that both groups spent the same amount of money, we can set the two expressions equal to each other:

`15x+15=3x+108\\12x=93\\x=7.75`

Because
`x` was the price of the book, which was asked for in the question, we conclude that the answer is $7.75.