Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A store offers a 20% discount on all items. If a customer uses a coupon for an additional 10% off the discounted price, what is the total percentage discount the customer receives?
- A28%
- B30%
- C38%
- D32%
Show answer & explanationAnswer & explanation
Correct answer: A. 28%
Let the original price be P. After the first 20% discount, the price is P * (1 - 0.20) = 0.80P. The additional 10% discount is applied to this new price: 0.80P * (1 - 0.10) = 0.80P * 0.90 = 0.72P. This means the final price is 72% of the original price. Therefore, the total discount is 100% - 72% = 28%.
Why the other options are wrong
- B. This is the incorrect result of simply adding the two discount percentages (20% + 10%), which is a common error.
- C. This is incorrect and likely results from a major miscalculation.
- D. This might result from an arithmetic error in the sequential calculation.
Successive Percentage Discounts
When multiple percentage discounts are applied sequentially, each subsequent discount is calculated on the *already discounted* price, not the original price.
- A discount of x% means multiplying by (1 - x/100).
- The order of discounts does not change the final price, but it's crucial to apply them one after another.
- Simply adding percentages will overstate the total discount.
Memory trick: Discount, then discount again, on the new price, my friend!