A car rental company charges $45 per day to rent a car and $0.30 per mile driven.
a) Write a rule for the total bill B as a function of the number of miles m the car is driven.
b) What is the bill for a one day rental if you drove 210 miles
The Correct Answer and Explanation is:
a) Rule for the Total Bill
To write a rule for the total bill ( B ) as a function of the number of miles ( m ), let’s break down the cost components:
- The car rental company charges a fixed fee of $45 per day.
- The company also charges $0.30 per mile driven.
Thus, the total bill ( B ) is the sum of the fixed daily fee and the variable charge based on the number of miles driven. This can be expressed as:
[
B(m) = 45 + 0.30m
]
Where:
- ( B(m) ) is the total bill in dollars.
- ( m ) is the number of miles driven.
b) Calculating the Bill for a One-Day Rental with 210 Miles Driven
To calculate the bill for renting the car for one day and driving 210 miles, we substitute ( m = 210 ) into the formula:
[
B(210) = 45 + 0.30 \times 210
]
First, multiply ( 0.30 \times 210 ):
[
0.30 \times 210 = 63
]
Now, add the fixed rental fee of $45:
[
B(210) = 45 + 63 = 108
]
Therefore, the total bill for renting the car for one day and driving 210 miles is $108.
Explanation
The total bill consists of two parts: a fixed daily rental fee and a variable charge based on the number of miles driven. The fixed fee of $45 applies regardless of how far the car is driven. The mileage fee, on the other hand, depends on the number of miles traveled. For each mile driven, the rental company charges $0.30. To calculate the total, we simply add the fixed cost of $45 to the mileage charge, which is ( 0.30 \times m ), where ( m ) is the number of miles driven. In this case, for 210 miles, the mileage charge is $63, and the total bill comes to $108.
This method of calculation helps in understanding how both fixed and variable components contribute to the final cost, ensuring the car rental service charges appropriately for the use of the vehicle over time and distance.