Sure, let's solve this step by step.
First, we need to determine the total cost Maya paid solely for the rental period, excluding any mileage costs:
- The daily rate for renting the car is [tex]$36.
- Maya rented the car for 4 days.
To find the total rental cost, multiply the daily rate by the number of days:
\[ \text{Rental cost} = 36 \, \text{\$[/tex]} \times 4 \, \text{days} = 144 \, \text{\[tex]$} \]
Next, we subtract the rental cost from the total amount Maya paid to find out how much she spent on additional miles beyond the free mileage:
- Total cost paid by Maya: $[/tex]174
- Rental cost: [tex]$144
\[ \text{Additional cost for mileage} = 174 \, \text{\$[/tex]} - 144 \, \text{\[tex]$} = 30 \, \text{\$[/tex]} \]
Now we calculate how many additional miles Maya drove, where each additional mile cost [tex]$0.20:
- Additional cost for mileage: $[/tex]30
[tex]\[ \text{Additional miles driven} = \frac{30 \, \text{\$}}{0.20 \, \text{\$/mile}} = 150 \, \text{miles} \][/tex]
Maya gets 200 miles for free. To find out the total number of miles she drove, we add these free miles to the additional miles:
- Free mileage: 200 miles
- Additional miles driven: 150 miles
[tex]\[ \text{Total miles driven} = 200 \, \text{miles} + 150 \, \text{miles} = 350 \, \text{miles} \][/tex]
Hence, Maya drove a total of 350 miles with the rented car.
