To determine the total cost for driving 150 miles with the given pricing structure, we're going to follow a step-by-step breakdown of how the charges are calculated.
1. Base fee and rates:
- The base fee charged by the rental car company is \[tex]$40.
- For the first 100 miles, the rate is \$[/tex]0.25 per mile.
- For any miles driven over 100 miles, the rate is \[tex]$0.18 per mile.
2. Miles driven:
- Total miles driven: 150 miles.
3. Calculating the charges:
- First, we calculate the cost for the first 100 miles:
\[
\text{Cost for the first 100 miles} = 40 + 0.25 \times 100
\]
- Here, 0.25 multiplied by 100 miles gives us \$[/tex]25.
- Adding the base fee, the total cost for the first 100 miles is:
[tex]\[
40 + 25 = 65 \text{ dollars}
\][/tex]
- Next, we calculate the cost for the miles over 100:
- In this case, the customer drives 150 miles, so the miles over 100 are:
[tex]\[
150 - 100 = 50 \text{ miles}
\][/tex]
- The cost for these additional 50 miles is:
[tex]\[
0.18 \times 50 = 9 \text{ dollars}
\][/tex]
- Adding the cost of the first 100 miles to the cost of the additional miles:
[tex]\[
\text{Total cost} = 65 + 9 = 74 \text{ dollars}
\][/tex]
Thus, if someone drives their rental car for 150 miles, they will owe the rental company \[tex]$74.00.
None of the listed options (\$[/tex]37.50, \[tex]$77.50, \$[/tex]67.00, \[tex]$27.00) are correct. The correct amount is \$[/tex]74.00.
