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Let's break down the given problem and find the formulas for the cost of renting cars from companies A, B, and C.

### Given:

- **Company A** charges 76 dollars per day with no mileage charge.
- **Company B** charges 15 cents per mile plus 39 dollars per day.
- **Company C** charges 5 cents per mile plus 57 dollars per day.

We need to express the cost as a function of the distance driven (denoted as \( x \) miles).

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### Part (a): Formulas for the cost

1. **For Company A**:  
   Since Company A charges a flat rate of 76 dollars per day without considering the miles driven, the formula for the cost \( y_A \) is constant.
   \[
   y_A = 76
   \]

2. **For Company B**:  
   Company B charges 15 cents per mile and 39 dollars per day. So, the cost \( y_B \) is a linear function of the miles driven:
   \[
   y_B = 0.15x + 39
   \]
   where \( x \) is the number of miles driven.

3. **For Company C**:  
   Company C charges 5 cents per mile and 57 dollars per day. Thus, the cost \( y_C \) is also a linear function of the miles driven:
   \[
   y_C = 0.05x + 57
   \]

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### Part (b): Graphing and intersections

For part (b), you will need to graph the three equations:
- \( y_A = 76 \)
- \( y_B = 0.15x + 39 \)
- \( y_C = 0.05x + 57 \)

The graph will show how the costs change as the distance driven (x) increases.

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Would you like me to help with graphing these equations and finding the intersection points? Or would you like further details on how these formulas were derived? Let me know if you need clarification.

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### 5 Related Questions:
1. How do you determine the slope of a linear cost function?
2. What does the intersection of two cost functions represent in terms of renting a car?
3. How would the cost formulas change if Company A charged by the mile?
4. What happens to the cost when no miles are driven for Company B and Company C?
5. How would you find the break-even point between two rental companies?

**Tip:** The slope in a linear cost function represents the rate of change of the cost with respect to miles driven, typically the cost per mile.

You need to rent a car and compare the charges of three different companies. Company A charges 76 dollars per day with no mileage charge. Company B charges 15 cents per mile plus 39 dollars per day. Company C charges 5 cents per mile plus 57 dollars per day. (a) Find formulas for the cost, in dollars, of driving cars rented from companies A, B, and C, in terms of x, the distance driven in miles in one day. (b) Graph all three functions on the same set of axes for 0 <= x <= 500. Report the x-coordinates of the two marked intersection points.

Learn how to compare rental car costs for three companies using linear equations. Formulas for Company A, B, and C are provided along with graphing and intersection points. Suitable for students in Grades 9-11.

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