Question

Rodrigo paid $60 for a jacket. The jacket was on sale for 25% off the original price. Rodrigo used a coupon for another 15% off the sale price.

emphasis,Part A,end emphasis,
To the nearest whole percentage, what was the overall percent discount that Rodrigo received on the jacket? Enter the answer in the box

emphasis,Part B,end emphasis,
To the nearest dollar, what was the original price of the jacket? Enter the answer in the box.

Answer 1

To solve this problem, we will go through each part step-by-step.

### Part A: Overall Percent Discount

1. **Calculate the Sale Price After the 25% Discount:**
Let \( P \) be the original price of the jacket. The sale price after a 25% discount can be expressed as:
\[
\text{Sale Price} = P - 0.25P = 0.75P
\]

2. **Calculate the Price After the 15% Coupon Discount:**
After applying an additional 15% discount on the sale price:
\[
\text{Final Price} = \text{Sale Price} - 0.15 \times \text{Sale Price} = 0.85 \times \text{Sale Price} = 0.85 \times 0.75P = 0.6375P
\]

3. **Set the Final Price Equal to the Amount Paid:**
Rodrigo paid $60. Therefore,
\[
0.6375P = 60
\]
To find \( P \):
\[
P = \frac{60}{0.6375} \approx 94.12
\]

4. **Calculate the Overall Discount:**
The overall discount can be calculated as follows:
\[
\text{Overall Discount} = P - \text{Final Price} = P - 60
\]
Now substituting \( P \):
\[
\text{Overall Discount} = 94.12 - 60 = 34.12
\]
The overall percentage discount is calculated as:
\[
\text{Overall Percent Discount} = \left(\frac{34.12}{P}\right) \times 100 \approx \left(\frac{34.12}{94.12}\right) \times 100 \approx 36.24\%
\]
Rounding to the nearest whole percentage:
\[
\text{Overall Percent Discount} \approx 36\%
\]

### Part B: Original Price

From our calculations in Part A, we found:
\[
P \approx 94.12
\]
Rounding to the nearest dollar gives us:
\[
\text{Original Price} \approx 94
\]

### Final Answers:
- **Part A: Overall Percent Discount**: 36%
- **Part B: Original Price**: $94