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 friends angus, who really loves to read, and discover that he has bought 19 books. angus received a $10 discount, but he still spent $5 more than alana and petra combined. how much does one book cost

Let's say the price of one book is the variable x
Therefore, Alana is 5x and Petra is 4x
Angus bought 19x, but since he had a $10 discount, it is 19x-10
Combined, Alana and Petra is 5x+4x, but since it says Angus spent $5 more, it would be 5x+4x+5
Therefore, we get the equation: 
19x-10=5x+4x+5
19x-10=9x+5
10x=15
x=15/10 or 3/2 which equals 1.5
Therefore, one book costs $1.5