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 determine the total bill for renting the car, we need to evaluate the different components of the bill:

1. **Car rental cost per day**: $27
2. **GPS rental cost per day**: $12.95
3. **Total gas cost when tanked**: 16 gallons × $3.70 per gallon

Let's calculate the total costs:

- Total car rental cost for **d** days:
- Car rental cost = \(27d\)

- Total GPS rental cost for **d** days:
- GPS rental cost = \(12.95d\)

- Total gas cost:
- Gas cost = \(16 \times 3.70 = 59.20\)

Now, we can put it all together to express the total bill **b** as a function of the number of days **d**:

\[
b(d) = 27d + 12.95d + 59.20
\]

Combining the terms gives:

\[
b(d) = (27 + 12.95)d + 59.20
\]
\[
b(d) = 39.95d + 59.20
\]

### a) Complete function rule
The function rule for the total bill \(b\) as a function of the days \(d\) the car is rented is:

\[
b = 39.95d + 59.20
\]

### b) Calculating the bill for a 9-day rental
Now, to find the total bill for a 9-day rental, plug \(d = 9\) into the function:

\[
b(9) = 39.95 \times 9 + 59.20
\]

Calculating each part:

\[
39.95 \times 9 = 359.55
\]
\[
b(9) = 359.55 + 59.20 = 418.75
\]

So, the total bill for a 9-day rental is:

**Total Bill for a 9-day rental: $418.75**