Question

Question content area topPart 1A 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 ​$3.70 per gallon. A car has a 16 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 9 day​ rental?Question content area bottomPart 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.dequalsenter your response herebplusenter your response hereB.bequalsenter your response heredplusenter your response hereC.bequalsenter your response heredD.dequalsenter your response hereb

Answer 1

To solve the problem, let's break it down step by step.

### a) Write a function rule for the total bill \( b \) as a function of the days \( d \) the car is rented.

1. **Daily rental cost for the car:** $27 per day. For \( d \) days, the cost will be \( 27d \).

2. **GPS rental cost:** $12.95 per day. For \( d \) days, the cost will be \( 12.95d \).

3. **Gas cost:** The car has a 16-gallon tank and gas costs $3.70 per gallon. So, the total cost for a full tank of gas is:
\[
3.70 \times 16 = 59.20
\]

Now, we can combine all these costs to write the function rule for the total bill \( b \):
\[
b = 27d + 12.95d + 59.20
\]

Combining the terms that involve \( d \):
\[
b = (27 + 12.95)d + 59.20
\]
\[
b = 39.95d + 59.20
\]

### Answer for part a:
The function rule is:
\[
b = 39.95d + 59.20
\]

### b) What is the bill for a 9-day rental?

Now we'll substitute \( d = 9 \) into the function:
\[
b = 39.95(9) + 59.20
\]
Calculating \( 39.95 \times 9 \):
\[
39.95 \times 9 = 359.55
\]
Now add the cost of gas:
\[
b = 359.55 + 59.20 = 418.75
\]

### Final Answer for part b:
The total bill for a 9-day rental is:
\[
b = 418.75
\]