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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.

ArithmeticPercentageDiscountsComparison
2025/3/10

1. Problem Description

The problem asks us to determine which is cheaper: a book with an original price of 19.99thatis2019.99 that is 20% off, or a book with an original price of 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,whichis19.99, which is 0.20 \times 19.99$. Then we subtract this discount amount from the original price.
The price of the first book after discount is:
19.99−0.20×19.99=19.99(1−0.20)=19.99(0.80)19.99 - 0.20 \times 19.99 = 19.99(1-0.20) = 19.99(0.80)
19.99(0.80)=15.99219.99(0.80) = 15.992
Next, we calculate the price of the second book after the discount. The discount amount is 10% of 17,whichis17, which is 0.10 \times 17$. Then we subtract this discount amount from the original price.
The price of the second book after discount is:
17−0.10×17=17(1−0.10)=17(0.90)17 - 0.10 \times 17 = 17(1-0.10) = 17(0.90)
17(0.90)=15.317(0.90) = 15.3
Now we compare the two prices: 15.99215.992 and 15.315.3. Since 15.3<15.99215.3 < 15.992, the second book is cheaper.

3. Final Answer

17(0.90)=15.317(0.90) = 15.3 is cheaper.

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