A rental car company rents cars for a flat fee of $20 and an hourly charge of $10.25. Therefore, the total cost CC to rent a car is a function of the hours tt the car is rented plus the flat fee.

Write the formula for the function that models this situation.

Find the total cost to rent a car for 2 days and 7 hours.

Determine how long the car was rented if the bill is $430

### 1. Writing the Function Formula

The total cost $ C $ to rent a car depends on the number of hours $ t $ the car is rented. The company charges a flat fee of $20 plus an hourly charge of $10.25. Thus, the function $ C(t) $ that models the total cost is given by:

\[
C(t) = 20 + 10.25t
\]

### 2. Finding the Total Cost for 2 Days and 7 Hours

First, we need to convert the rental time from days and hours into total hours.

- 2 days = 2 \times 24 = 48 hours
- Additional 7 hours

Total hours $ t = 48 + 7 = 55 $ hours.

Now, we substitute $ t = 55 $ into the function:

\[
C(55) = 20 + 10.25 \times 55
\]

Calculating this:

\[
C(55) = 20 + 563.75 = 583.75
\]

So, the total cost to rent a car for 2 days and 7 hours is **$583.75**.

### 3. Determining the Rental Duration for a Bill of $430

To find out how long the car was rented if the bill is $430, we set $ C(t) = 430 $ and solve for $ t $:

\[
430 = 20 + 10.25t
\]

Subtract 20 from both sides:

\[
410 = 10.25t
\]

Divide both sides by 10.25 to solve for $ t $:

\[
t = \frac{410}{10.25}
\]

Calculating $ t $:

\[
t \approx 40
\]

So, the car was rented for **40 hours**.

### Summary

1. **Function Formula**: $ C(t) = 20 + 10.25t $
2. **Cost for 2 days and 7 hours**: $583.75
3. **Rental duration for a $430 bill**: 40 hours

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Would you like any more details or have any questions?

Here are some additional related questions:

1. What would the total cost be if the car is rented for 5 hours?
2. If a customer has a budget of $150, for how many hours can they rent the car?
3. How much would it cost to rent a car for 1 day and 4 hours?
4. If the hourly rate increases to $12, what would be the new formula for the cost?
5. How would the function change if the flat fee were removed?

**Tip**: When solving equations, always isolate the variable you need to solve for by performing the same operation on both sides of the equation.

Learn how to calculate the total cost to rent a car based on a flat fee of $20 and an hourly charge of $10.25. Includes examples like finding the cost for 2 days and 7 hours and determining rental duration for a $430 bill. Suitable for Grades 7-9.

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