https://file.aiquickdraw.com/mathbot/file/17260555235038o25h21f.jpg

The problem in the image involves a car rental scenario. Here's a breakdown of the questions:

**Given:**
- A car rental company charges a daily fee of $50 plus an additional $0.15 per kilometer driven.

### **a) Express the daily rental cost as a function of the number of kilometers traveled.**

Let's define:
- $ C(k) $ as the daily rental cost in dollars.
- $ k $ as the number of kilometers driven.

The daily rental cost is composed of a fixed cost of $50 plus a variable cost of $0.15 per kilometer driven. So, the function can be expressed as:

\[
C(k) = 50 + 0.15k
\]

### **b) Determine the rental cost if you drive 472 km in one day.**

To find the cost for driving 472 km, substitute $ k = 472 $ into the function:

\[
C(472) = 50 + 0.15 \times 472
\]

Calculating this:

\[
C(472) = 50 + 70.8 = 120.8
\]

So, the rental cost for driving 472 km in one day is **$120.80**.

### **c) Determine how far you can drive in a day for $80.**

To find the distance $ k $ you can drive for a total cost of $80, set $ C(k) = 80 $ and solve for $ k $:

\[
80 = 50 + 0.15k
\]

Subtract 50 from both sides:

\[
30 = 0.15k
\]

Now, divide by 0.15:

\[
k = \frac{30}{0.15} = 200
\]

So, you can drive **200 kilometers** in a day for $80.

### Would you like more details, or do you have any questions?

#### Related Questions:
1. How would the function change if the daily rate increased to $60?
2. What would be the cost for driving 300 km?
3. How would the maximum distance change if the total cost allowed was increased to $100?
4. If you only have $70 to spend, how far could you drive?
5. What is the cost per kilometer driven when the total cost is $150?

#### Tip:
When solving cost problems like this, always separate fixed costs from variable costs to easily set up your equations.

A company rents cars for $50 per day plus $0.15/km. a) Express the daily rental cost as a function of the number of kilometers traveled. b) Determine the rental cost if you drive 472 km in one day. c) Determine how far you can drive in a day for $80.

Solve a real-life math problem where a car rental costs $50 per day plus $0.15 per kilometer driven. Calculate rental cost for driving 472 km or determine how far you can drive for $80. Suitable for Grades 7-9 students learning about linear functions and algebra.

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