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

To determine the original price of the dress before successive 25% reductions to a final price of $18, reverse the percentage decreases and divide $18 by 0.75 squared. The original price is found to be $32.

Step-by-step explanation:

The original price of the dress can be found by calculating the inverse of the successive percentage decreases.

When the dress price is reduced by 25%,

we can represent the new price as 75% of the original price (100% - 25% = 75%).

To make the calculation easier, we represent this percentage as a decimal, which is 0.75.

After a second reduction of 25%, the remaining value is again 75% of the intermediate price.

This means the $18 is 75% of 75% of the original price. So, we can set up the equation as:

0.75 (0.75 × original price) = $18

This simplifies to 0.75² × original price = $18

Now, divide both sides of the equation by 0.75² to find the original price:

original price = $18 / 0.75²

original price = $18 / 0.5625

original price = $32

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