Question content area top

Question

Part 1
A car rental agency charges ​$27 per day to rent a car and ​$12.95 per day for a global positioning system​ (GPS). Customers are charged for their full tank of gas at ​$3.80 per gallon. A car has a 11 gallon tank and a GPS.
​a) Write a function rule for the total bill b as a function of the days d the car is rented.
​b) What is the bill for a 10 day​ rental?
Question content area bottom
Part 1
​a) Choose the correct function rule for the total bill b as a function of the days d the car is rented.
​(Type an integer or a​ decimal.)
A.
dequals
  
enter your response hereb
B.
dequals
  
enter your response herebplus
  
enter your response here
C.
bequals
  
enter your response heredplus
  
enter your response here
D.
bequals
  
enter your response hered

Answer 1

To write a function rule for the total bill \( b \) as a function of the number of days \( d \) the car is rented, we need to consider each component of the cost:

1. Car rental cost per day: $27 per day
2. GPS rental cost per day: $12.95 per day
3. Gas cost: The car has a 11-gallon tank, and if you fill it up, it costs $3.80 per gallon.

First, we can calculate the gas cost: \[ \text{Gas cost} = \text{Price per gallon} \times \text{Gallons} = 3.80 \times 11 = 41.80 \] Now, we can find the total daily rental cost: \[ \text{Total daily rental cost} = \text{Cost of car rental per day} + \text{Cost of GPS per day} = 27 + 12.95 = 39.95 \]

Now, the total bill \( b \) can be expressed as: \[ b = (\text{Total daily rental cost} \times d) + (\text{Gas cost}) \] Substituting the values: \[ b = (39.95 \times d) + 41.80 \]

Part 1: Function Rule

So the function rule for the total bill \( b \) as a function of the days \( d \) the car is rented is: \[ b = 39.95d + 41.80 \]

Part 2: Bill for a 10-day Rental

To find the bill for a 10-day rental, substitute \( d = 10 \): \[ b = 39.95 \times 10 + 41.80 \] Calculating this gives: \[ b = 399.50 + 41.80 = 441.30 \]

Final Answers:

a) The function rule is: \[ b = 39.95d + 41.80 \]

b) The bill for a 10-day rental is: \[ b = 441.30 \]

Answer 2

What is the bill for a 10 day​ rental?
​$
  
enter your response here

Answer 3

To calculate the bill for a 10-day rental using the function we derived earlier, we substitute \( d = 10 \) into the function:

\[ b = 39.95d + 41.80 \]

Substituting \( d = 10 \): \[ b = 39.95 \times 10 + 41.80 \] Calculating that: \[ b = 399.50 + 41.80 = 441.30 \]

Therefore, the bill for a 10-day rental is: \[ \text{Bill} = \boxed{441.30} \]

So you would enter: \[ \text{$441.30} \]