Alana and Petra go to a used book sale, where every book is the same price. Alana buys 5 books and Petra buys 4 books. They run into their friend Angus, who really loves to read, and discover that he has bought 19 books. Angus received a $10 discount, but he still spent $7.50 more than Alana and Petra combined. How much does one book cost?

Question

Alana and Petra go to a used book sale, where every book is the same price. Alana buys 5 books and Petra buys 4 books. They run into their friend Angus, who really loves to read, and discover that he has bought 19 books. Angus received a $10 discount, but he still spent $7.50 more than Alana and Petra combined. How much does one book cost?

Answer 1

Let the cost of one book be x dollars.

Alana bought 5 books, so she spent 5x dollars.
Petra bought 4 books, so she spent 4x dollars.
Angus bought 19 books, so he spent 19x dollars.

Angus received a $10 discount, so he paid 19x - 10 dollars.

According to the given information, Angus spent $7.50 more than Alana and Petra combined:
19x - 10 = 5x + 4x + 7.50
19x - 10 = 9x + 7.50
19x - 9x = 10 + 7.50
10x = 17.50
x = 1.75

So, one book costs $1.75.