LET'S DRIVE THE BEST BARGAIN

Class: Algebra (grades 7-12, possible use with Pre-Algebra with more backgrounding)

Materials: Graph paper, colored pencils or pens, rulers, mileage maps, pencil, and paper.

Goals:Construct a data table, determine a reasonable scale for the graph, graph the corresponding information for each rental car company, look for patterns, ability to read mileage maps, and make conclusions from the graph.

Time Required: Two days.

Background: Students should be able to plot points on a Cartesian plane, read mileages from
maps, read and interpret data from a Cartesian graph.

Setting:There are three car rental agencies in town: Brakefast, Collision, and Deadend. Your family is given you the responsibility of choosing the best deal for each of the day trips you will take over the summer vacation. A day trip is considered to be a trip where you leave home, go to your destination, and return from your destination in the same day. Which agency do you use for your trip? A United States mileage map and the rates for each agency are given.

Problem:Your family has given you the job of determining which car rental company to use for 3 upcoming day trips your family will be taking this summer. Your objective is to save your family money. Which agency will you use for each trip?

The companies are listed below along with their rates and a mileage map of the United States is included. Do not forget to use the round trip mileage for your total. Your first trip should be less than 100 miles, the second trip should be between 100 and 200 miles, and your last trip should be over 250 miles. In your written document you should tell the destination of the trip, explain your route, and show how you calculated your total cost.

Evaluation:Each group should produce a document (either written, typed, or computer generated) showing assumptions and calculations that justify its conclusions. There should be a graph for each rental company representing the cost per mile traveled. Is the graph designed in such a way that logical conclusions are drawn from it? Is an appropriate or inappropriate scale used?

Extensions:

A.Your daughter (sister) wants to bring a friend along. This will cause you to need to rent the next larger size vehicle. The friend agrees to pay 1/5 of the mileage charge but can afford no more. Consult the accompanying Rate increase chart to graph the adjusted cost of the rented vehicle and decide how this will affect your choice of rental companies. Make graphs to help support your conclusions.

Company	Daily Rate for Next Size Category of Car	Cost Per Mile for Next Category of Car
Brakefast	$32.00	$.35 per mile over 100 miles
Collision	$30.00	$.40 per mile over 80 miles
Deadend	$50.00	$.50 per mile over 150 miles

B.Plan a four day trip of between 350 and 800 miles. You must visit at least four different sites. Note that mileage on a several day trip is cumulative (not monitored on a daily basis). Using graphs to help in the decision process, again select the company you would do business with.

C.Investigate the rate tables for several local car rental companies. Chart the rates for different sized cars. Describe what you believe to be the rate structure for each company. Develop a rationale for a rate structure for U-Drive Rent-All.
Scoring:
Entire paper is neat, legible and well-organized (1 point), written explanations are effective and comprehensive (3 points), computations are correct (3 points).

Teacher Notes:
You can suggest scales for the axes, you can choose 3 distances (round trip) to illustrate
that each rental company has the potential to be the leasexpensive.

Problem:You have three days of vacation and have decided to take three different day trips. A day trip is a trip where you leave home, go to your destination and return home that same day. You will need to rent a car and there are three rental agencies in town. Your objective is to spend the least amount on the rental car.

Directions:The rates for the car rental agencies are given in the table below. You will be given a map. The first trip should be less than 100 miles, the second trip should be between 100 and 200 miles and the last trip should be over 250 miles. You are to make a graph on a rectangular coordinate system showing the cost per mile traveled for each rental car. Each group must produce a written document that tells the destination of the trip, the route taken, and how the cost was determined.

Company	Cost per day	Cost per mile
Brakefast	$30.00	$.30 per mile over 100 miles
Collision	$25.00	$.40 per mile over 80 miles
Deadend	$50.00	$.50 per mile over 200 miles

Evaluation:Each group should show their assumptions and the calculations that justify your conclusions. Your graph should be designed so that you use appropriate scales and logical conclusions can be drawn from it.

Scoring:Entire paper is neat, legible and well-organized. (1 point)
Written explanations are effective and comprehensive. (3 points)
Computations are correct. (3 points)
Graph is clear and accurate. (3 points)

The first part should include the destination of their trip, a description or map of the route taken, the following chart and a description of how they determined the cost of the trip. If they chose a trip of 140 miles, the information from the graph indicates a cost of a little over $41 is the cheapest cost with the Brakefast Company. Showing the actual calculations would determine that the cost was $30 plus 40 miles times $.30 cents per mile or $42.

The solution for the extensions should include a re-drawn graph and all of the elements present in the original solution. The following graph shows the costs for the larger car needed in one of the extensions.