Question
The price of a dress is reduced by 50%. When the dress still does not sell, it is reduced by 50% of the reduced price. If the price of the dress after both reductions is $75, what was the original price?
Question content area bottom
Part 1
The original price of the dress was $
enter your response here.
(Type an integer or a decimal.)
Question content area bottom
Part 1
The original price of the dress was $
enter your response here.
(Type an integer or a decimal.)
Answers
GPT-4o mini
Let's denote the original price of the dress as \( P \).
1. The first reduction is 50% of the original price:
\[
\text{First reduced price} = P - 0.5P = 0.5P.
\]
2. The second reduction is also 50%, but this time it is on the already reduced price:
\[
\text{Second reduced price} = 0.5P - 0.5 \times 0.5P = 0.5P - 0.25P = 0.25P.
\]
According to the problem, the price after both reductions is $75. Therefore, we have:
\[
0.25P = 75.
\]
To find \( P \), we can multiply both sides by 4:
\[
P = 75 \times 4 = 300.
\]
Thus, the original price of the dress was \(\boxed{300}\) dollars.
1. The first reduction is 50% of the original price:
\[
\text{First reduced price} = P - 0.5P = 0.5P.
\]
2. The second reduction is also 50%, but this time it is on the already reduced price:
\[
\text{Second reduced price} = 0.5P - 0.5 \times 0.5P = 0.5P - 0.25P = 0.25P.
\]
According to the problem, the price after both reductions is $75. Therefore, we have:
\[
0.25P = 75.
\]
To find \( P \), we can multiply both sides by 4:
\[
P = 75 \times 4 = 300.
\]
Thus, the original price of the dress was \(\boxed{300}\) dollars.