# Linear Equation

You begin by contacting two car rental companies, Avis and Enterprise. Avis offers a midsize car for $64.99 per day with unlimited mileage. This means that for this rental the number of miles driven does not impact on the cost. Enterprise offers a midsize car for $ 45.87 per day with 150 miles free. But each mile beyond 150 that the car is driven cost $0.25. It is clear that Enterprise offers the better deal if the car is driven fewer than 150 miles. But what if the car is driven more than 150 miles? At what point will the Avis rental become a better deal? Let’s analyze the situation. Let x denote the number of miles the car is driven.

1. Suppose A is the cost of renting at Avis. Find a linear equation involving A and x.

2. Now let E be the cost of renting at Enterprise. Find a linear equation involving E and x, if x ≤ 150. Find a linear equation involving E and x, if x > 150.

3. Graph the linear Equations found in part (1) and (2) on the same set of coordinate axes. Be careful about the restrictions on x for the equations found in part (2).

4. Find the mileage beyond which the Avis rental is more economical by finding the point of intersection of the two graphs. Label this point on this graph.

5. Explain how you can use the solution to part (4) to decide on which car rental is more economical.

6. In an effort to find an even better deal, you contact Auto Save Rental. They offer a midsize car for $36.99 per day with 100 miles free. Each mile driven over 100 miles costs $0.25. Find equation(s) that involve the cost S at Auto Save Rental and the miles x driven.

7. Graph this equation on the same graph found in part (3).

8. It should be clear that Auto Save Rental is the best choice among the three if you are driving less than 100 miles. For what values of x, if any, do Avis or Enterprise offer a better deal?

9. Still not sure you have the best deal, you call Usave Car Rental. They offer a midsize car for $35.99 per day with 200 free miles. Each mile over 200 costs $0.25. Find an equation for the cost U at Usave and graph it on the same graph found on the part (7).

10. For what values of x, if any, is Usave the best deal?

11. Discuss your choice of car rental companies if you think you will drive between 125 and 175 miles.

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