Question

The price of a dress is reduced by 25​%. When the dress still does not​ sell, it is reduced by 25​% of the reduced price. If the price of the dress after both reductions is ​$18​, what was the original​ price?The price of a dress is reduced by 25​%. When the dress still does not​ sell, it is reduced by 25​% of the reduced price. If the price of the dress after both reductions is ​$18​, what was the original​ price?

A) $32
B) $40
C) $48
D) $36

Answer 1

The original price of the dress was calculated by dividing $18 by the percentage reduction squared (25% reduced twice equals 0.5625 when expressed as a decimal), resulting in an original price of $32.

Step-by-step explanation:

To find the original price of the dress, we need to work backwards from the final price of $18 after both reductions. Let's assume the original price is x.

First, the price is reduced by 25%. This means it becomes 75% of the original price, or 0.75x.

Then, the reduced price is further reduced by 25% of the reduced price. This means it becomes 75% of 0.75x, or 0.75 * 0.75x = 0.5625x.

Finally, we can set up the equation:

0.5625x = 18

Dividing both sides by 0.5625 gives us:

x = 18 / 0.5625

x = 32

Therefore, the original price of the dress was $32.