To determine the total amount you need to pay for a restaurant bill given a tax rate and a tip percentage, we'll follow these steps:
1. Calculate the tax amount:
- The original bill amount is \[tex]$73.25.
- The tax rate is \(7 \frac{1}{2} \% \) which is equivalent to 7.5%.
- To find the tax amount, multiply the bill amount by the tax rate:
\[
\text{Tax amount} = \$[/tex]73.25 \times \frac{7.5}{100} = \[tex]$5.49375
\]
2. Calculate the amount after adding the tax:
- Add the tax amount to the original bill amount:
\[
\text{Amount after tax} = \$[/tex]73.25 + \[tex]$5.49375 = \$[/tex]78.74375
\]
3. Calculate the tip amount:
- The tip rate is 15%.
- To find the tip amount, multiply the original bill amount by the tip rate:
[tex]\[
\text{Tip amount} = \$73.25 \times \frac{15}{100} = \$10.9875
\][/tex]
4. Calculate the total amount:
- Add the tip amount to the amount after tax:
[tex]\[
\text{Total amount} = \$78.74375 + \$10.9875 = \$89.73125
\][/tex]
Given these calculations, the total amount you need to pay is \[tex]$89.73125, corresponding to the nearest option:
c. \$[/tex]89.73
Therefore, the correct answer is c. [tex]\( \$89.73 \)[/tex].
