Question

Nathan took his car in for service and repairs. He had a coupon for 15% off.

Original Prices
• Labor $299.34
• Parts $384.42
• Other $68.07

Which amount is closest to Nathan's total costs after the 15% discount and including 7% sales tax? [Assume tax is applied after the discount is applied.]

Answer 1

To find Nathan's total costs after the 15% discount and including a 7% sales tax, we can follow these steps:

1. **Calculate the total original cost:**
\[
\text{Total Original Cost} = \text{Labor} + \text{Parts} + \text{Other}
\]
\[
\text{Total Original Cost} = 299.34 + 384.42 + 68.07 = 751.83
\]

2. **Calculate the discount amount:**
\[
\text{Discount} = 15\% \text{ of Total Original Cost}
\]
\[
\text{Discount} = 0.15 \times 751.83 = 112.77
\]

3. **Calculate the total cost after the discount:**
\[
\text{Total After Discount} = \text{Total Original Cost} - \text{Discount}
\]
\[
\text{Total After Discount} = 751.83 - 112.77 = 639.06
\]

4. **Calculate the sales tax on the discounted amount:**
\[
\text{Sales Tax} = 7\% \text{ of Total After Discount}
\]
\[
\text{Sales Tax} = 0.07 \times 639.06 = 44.73
\]

5. **Calculate the total cost after tax:**
\[
\text{Total Cost After Tax} = \text{Total After Discount} + \text{Sales Tax}
\]
\[
\text{Total Cost After Tax} = 639.06 + 44.73 = 683.79
\]

Thus, Nathan's total costs after the 15% discount and including 7% sales tax is approximately **$683.79**.