The problem asks us to determine which is cheaper: a book with an original price of $19.99 that is 20% off, or a book with an original price of $17 that is 10% off.

1. Problem Description

The problem asks us to determine which is cheaper: a book with an original price of $19.99 that is 20$17 that is 10% off.

2. Solution Steps

First, we calculate the price of the first book after the discount. The discount amount is 20% of $19.99, which is$0.20 \times 19.99$. Then we subtract this discount amount from the original price.

The price of the first book after discount is:

$19.99 - 0.20 \times 19.99 = 19.99(1-0.20) = 19.99(0.80)$

$19.99(0.80) = 15.992$

Next, we calculate the price of the second book after the discount. The discount amount is 10% of $17, which is$0.10 \times 17$. Then we subtract this discount amount from the original price.

The price of the second book after discount is:

$17 - 0.10 \times 17 = 17(1-0.10) = 17(0.90)$

$17(0.90) = 15.3$

Now we compare the two prices: $15.992$ and $15.3$. Since $15.3 < 15.992$, the second book is cheaper.

3. Final Answer

$17(0.90) = 15.3$ is cheaper.