Question

A student qualifies for six different tuition discounts: 20%, 15%, 23%, 5%, 3%, and 1%. She is confused and wants to know what single discount percent she is receiving. What should the college tell her?

A) 20%
B) 15%
C) 23%
D) The college should explain that she is receiving a single discount of 67%.

Answer 1

The college should explain that tuition discounts are compounded, not simply added together. Each discount is applied to the amount after the previous discount, so the overall discount rate is not the sum of the individual percentages.

Step-by-step explanation:

The question pertains to calculating a combined discount rate from multiple tuition discounts. Contrary to choosing a single percentage, we need to understand that discounts are compounded, not simply added. This means that each subsequent discount is applied to the reduced amount after the previous discount has been taken. Therefore, the college should explain the compounding effect of multiple discounts rather than indicating a single sum of percentages.

To find the overall discount:

1. Start with an initial amount (let's say $100 for ease of calculation).
2. Applying the 20% discount reduces the amount to $80.
3. Then, a 15% discount on $80 reduces it by $12, bring the amount to $68.
4. Continue this process with the other discounts.
5. The final amount will reveal the total percentage reduction from the original price.

Thus, the single discount rate is not just the sum of individual rates (which would incorrectly suggest a 67% discount), but rather a compounded rate resulting in a different overall percentage.