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? \( \$ 2.50 \) \$ \( \$ 19.75 \) \( \$ 0.25 \) \( \$ 1.75 \)

Let the price of one book be \( x \). Alana's spending would be \( 5x \) and Petra's spending would be \( 4x \). So the total spending of Alana and Petra combined is: \[ 5x + 4x = 9x \] Angus bought 19 books, so he would normally spend \( 19x \). With the $10 discount, the equation for Angus's spending becomes: \[ 19x - 10 \] According to the problem, Angus spent \( \$7.50 \) more than the combined spending of Alana and Petra: \[ 19x - 10 = 9x + 7.50 \] Now we can solve for \( x \): 1. Rearranging gives us: \[ 19x - 10 - 9x = 7.50 \] \[ 10x - 10 = 7.50 \] 2. Adding 10 to both sides: \[ 10x = 17.50 \] 3. Dividing by 10: \[ x = 1.75 \] Thus, the cost of one book is \( \$ 1.75 \).