Question
Ahotel manager found that his gross receipts for the day, including a \( 9 \% \) sales tax, were \( \$ 2488.47 \). Find the amount of sales tax collected. What was the sales tax?
Ask by Hammond Huang. in the United States
Dec 29,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The sales tax collected was approximately \$205.47.
Solution
To determine the amount of sales tax collected, we can break down the problem as follows:
1. **Understand the Total Amount:**
- The total gross receipts including a 9% sales tax are **\$2,488.47**.
- Let’s denote the original sales amount before tax as **\( x \)**.
2. **Set Up the Equation:**
- The total amount is the sum of the original sales and the sales tax:
\[
\text{Total} = x + 0.09x = 1.09x
\]
- So,
\[
1.09x = 2488.47
\]
3. **Solve for \( x \):**
- Divide both sides by 1.09 to find the original sales amount:
\[
x = \frac{2488.47}{1.09} \approx 2283.00
\]
4. **Calculate the Sales Tax:**
- The sales tax is 9% of the original sales amount:
\[
\text{Sales Tax} = 0.09 \times 2283.00 = 205.47
\]
**Therefore, the sales tax collected was approximately **\$205.47**.
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Simplify this solution The Deep Dive
To find the amount of sales tax collected, we can use the formula for gross receipts: \[ \text{Gross Receipts} = \text{Sales Amount} + \text{Sales Tax} \] Where Sales Tax is \( 9\% \) of the Sales Amount. Let \( x \) be the Sales Amount. Therefore, we can express the gross receipts as: \[ 2488.47 = x + 0.09x = 1.09x \] To find \( x \), we rearrange the equation: \[ x = \frac{2488.47}{1.09} \approx 2280.05 \] Now, we can find the sales tax: \[ \text{Sales Tax} = 0.09 \times 2280.05 \approx 204.21 \] Thus, the amount of sales tax collected is approximately **\$204.21**.
