Answer :
To solve the problem of determining a reasonable estimate for the total amount Romeo paid for his car repairs, we can follow these steps:
1. Identify the Repair Cost: The initial cost of the car repairs is [tex]$380.75.
2. Determine the Sales Tax Rate: The sales tax rate is specified as 7.5%.
3. Calculate the Sales Tax Amount:
- To find the sales tax amount, you multiply the repair cost by the sales tax rate.
- \( \text{Sales Tax} = 380.75 \times 0.075 = 28.55625 \)
4. Calculate the Total Cost:
- Add the sales tax amount to the initial repair cost to find the total cost.
- \( \text{Total Cost} = 380.75 + 28.55625 = 409.30625 \)
Since the total calculated cost is approximately $[/tex]409.31, let's look at the provided answer choices:
- A. [tex]$28.50 (This is too low and only represents the sales tax amount, not the total cost.)
- B. $[/tex]410.00 (This is very close to our calculated total and is a reasonable estimate.)
- C. [tex]$352.50 (This is lower than the initial repair cost, so it's not possible after adding sales tax.)
- D. $[/tex]442.00 (This amount is higher than our calculated total.)
Given these choices, option B: $410.00 is the most reasonable estimate for the total amount Romeo paid to repair his car.
1. Identify the Repair Cost: The initial cost of the car repairs is [tex]$380.75.
2. Determine the Sales Tax Rate: The sales tax rate is specified as 7.5%.
3. Calculate the Sales Tax Amount:
- To find the sales tax amount, you multiply the repair cost by the sales tax rate.
- \( \text{Sales Tax} = 380.75 \times 0.075 = 28.55625 \)
4. Calculate the Total Cost:
- Add the sales tax amount to the initial repair cost to find the total cost.
- \( \text{Total Cost} = 380.75 + 28.55625 = 409.30625 \)
Since the total calculated cost is approximately $[/tex]409.31, let's look at the provided answer choices:
- A. [tex]$28.50 (This is too low and only represents the sales tax amount, not the total cost.)
- B. $[/tex]410.00 (This is very close to our calculated total and is a reasonable estimate.)
- C. [tex]$352.50 (This is lower than the initial repair cost, so it's not possible after adding sales tax.)
- D. $[/tex]442.00 (This amount is higher than our calculated total.)
Given these choices, option B: $410.00 is the most reasonable estimate for the total amount Romeo paid to repair his car.
