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?

The price of the book is $7.75.

Step-by-step explanation:

Let's first establish an equation.

If I buy a book costing dollars and a bookmark costing 1 dollars, I will have spent dollars. So a group of 15 people doing the same will have spent dollars.

Analogously, the group of 3 people has spent dollars.

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

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