## Fun and SunRent-A-Car

The Green family is planning a one-week vacation in Florida and needs to rent a car while there. They researched and found the following options.

 *Weekly Rate 1 *Weekly Rate 2 \$329 per week, unlimited mileage. \$219 per week, plus 12 cents per mile. *Partial week charged at a full week's price. \$50 per day, unlimited mileage. \$40 per day plus 3 cents per mile. **Partial days charged at a full day's price.

The Greens don't know exactly how far they will drive but estimate that it will be between 500 and 1000 miles. They must decide which plan to choose. Explore the four options below.

### Make a Table (Offline)

Fill in a table like the one below with the costs of each option.

Comparison of Total Rental Car Costs per Week Based on Mileage Driven
Total Miles Driven in Week 500 600 700 800 900 1000
Cost at Weekly Rate 1
Cost at Weekly Rate 2
Cost at Daily Rate 1
Cost at Daily Rate 2

### Make a Graph (Offline)

Draw and compare graphs of the four options on axes like the ones below.

### Analyze the Graph

1. Each graph contains six points. Is it appropriate to connect the points on the graphs to make lines? Explain why or why not.
2. Do all of the points of each graph lie on a straight line? What is a function called that has a graph which is a straight line?
3. Which of the lines is steepest? What is the slope of that line? Which of the functions grows at the fastest rate? Which of the functions grows at the slowest rate? What is its slope ?
4. If you extend the lines through the y axis, would any of the lines go through the origin? Explain why or why not.
5. What is significant about the points where the graphs intersect?

### Write the Functions

Write the Total Week's Rental Car Cost as a function of the Number of Miles Driven for each of the options.

### Write a Paragraph

Based on the best economics, explain under what conditions the Green Family should choose each option.

### Extension 1

The Greens know that they will drive approximately 900 miles, but they don't know exactly how long they will be in Florida, only that it will be sometime between 3-8 days. Given these new circumstances, explain under what conditions they should choose each option.

### Extension 2

The Greens don't know exactly how long they will be in Florida, only that it will be sometime between 3-8 days. They also don't know exactly how far they will drive, only somewhere between 500-1000 miles. Given these new circumstances, explain under what conditions they should choose each option.

 Check here for Teachers' Notes

More Math Activities by Cynthia Lanius

lanius@math.rice.edu
URL http://math.rice.edu/~lanius/Algebra/rentacar.html