Question
Joyce paid \( \$ 81.00 \) for an item at the store that was 55 percent off the original price. What was the original price? Give your answer tō the nearest cent. \( > \) Next Question
Ask by Gardner Mejia. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The original price was \$180.00.
Solution
To determine the original price of the item before the discount, follow these steps:
1. **Understand the Discount:**
- **Discount Given:** 55% off
- **Amount Paid by Joyce:** \$81.00
A 55% discount means Joyce paid **45%** of the original price (since 100% - 55% = 45%).
2. **Set Up the Equation:**
Let \( P \) be the original price.
\[
0.45 \times P = 81.00
\]
3. **Solve for \( P \):**
\[
P = \frac{81.00}{0.45}
\]
\[
P = 180.00
\]
4. **Conclusion:**
The original price of the item was **\$180.00**.
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Simplify this solution Bonus Knowledge
To find the original price, we can use the formula for discounts. If Joyce paid \( \$ 81.00 \) for an item that was 55% off, it means she paid 45% of the original price. We can set up the equation: \( 0.45 \cdot \text{Original Price} = 81.00 \). Solving for the original price, we get \( \text{Original Price} = \frac{81.00}{0.45} \), which equals \( \$ 180.00 \). So, the original price of the item was \( \$ 180.00 \).
