https://file.aiquickdraw.com/mathbot/file/1727294899760sqwo840q.jpg

To solve this problem:

1. **Compute the tax:**
   - The purchase amount is $545.42.
   - The sales tax rate is 9.9%.
   - The formula for the sales tax is:
     \[
     \text{Sales Tax} = \text{Purchase Amount} \times \frac{\text{Sales Tax Rate}}{100}
     \]
     Plugging in the values:
     \[
     \text{Sales Tax} = 545.42 \times \frac{9.9}{100} = 545.42 \times 0.099
     \]
     Calculating this:

     \[
     \text{Sales Tax} \approx 53.00
     \]

2. **Compute the total cost of the purchase:**
   - The total cost is the sum of the original purchase price and the sales tax:
     \[
     \text{Total Cost} = \text{Purchase Amount} + \text{Sales Tax}
     \]
     Substituting the values:
     \[
     \text{Total Cost} = 545.42 + 53.00 = 598.42
     \]

So, the answers are:
- **Sales tax:** \$53.00
- **Total cost:** \$598.42

Let me know if you have any questions or if you'd like further details! Here are some related questions:

1. How would the calculations change if the tax rate was different?
2. Can you explain why we multiply by 0.099 for the tax rate?
3. What would the total cost be if no tax was applied?
4. How does rounding to the nearest cent affect the final result?
5. What is the impact of compounding taxes (like state and local) on purchases?

**Tip:** Always double-check rounding instructions, as they can slightly alter results, especially in financial calculations.

Suppose you make a purchase for $545.42. The sales tax for this purchase is 9.9%. Compute the tax. Round your answer to the nearest cent. Compute the cost of the purchase. Round your answer to the nearest cent.

Learn how to compute the sales tax for a $545.42 purchase with a 9.9% tax rate. This problem demonstrates the application of percentages in calculating taxes and determining the total cost. Suitable for students in Grades 6-8.

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