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 original price of the dress was $___(Round to the nearest dollar as needed.)

Answer 1

Working backwards from the final reduced price of $18, the original price of the dress is calculated by reversing the 25% reductions. After finding the price post-first reduction ($24), the original price is determined to be $32.

Step-by-step explanation:

To find the original price of the dress, we need to work backward from the final reduced price. The dress was first reduced by 25%, and then it was reduced by another 25% of the reduced price and sold for $18.

Let's denote the price after the first reduction as x. Since the second reduction was 25% of this intermediate price, we can write this as 0.75x = $18. Solving for x gives us the price after the first discount: x = $18 / 0.75 = $24.

To find the original price, we recognize that $24 is 75% (100% - 25% reduction) of the original price, so we let y be the original price and we have 0.75y = $24. Solving for y, the original price, gives us y = $24 / 0.75 = $32. Therefore, the original price of the dress was $32 when rounded to the nearest dollar.