Car Quest - Systems of Equations

Car Quest - Systems of EquationsAn Algebra WebQuest Introduction
Americans are dependent on their cars to get them to school, work, and everywhere else they need to go in the course of their daily lives.  Your family is no exception.  Recently, your family car stopped running and you are in the market for a new vehicle.

Your challenge will be to find a car or truck that will be cost effective to purchase and cost effective to operate.  Using the cost of the vehicle, the annual cost of gas, and the annual cost of insurance you will analyze which vehicle is the best choice for your family.


Your task is to research different vehicles and collect data about purchase prices and total cost of ownership (including gas and insurance). Using this information and your algebra skills, you will find the break even point for the two vehicles you will choose.  You will then analyze this information to make a decision about which vehicle your family should buy.

Step 1 (Purchase Price):
Your first decision will be to research new or used vehicles.  Once you have settled the "new or used" quesiton, research vehicles using car manufacturer websites or used car websites like Vehix, AutoTrader, and  You will need to choose two different vehicles and determine the purchase price.  Record this information on the Datasheet Handout and print the page you are using to determine the price of the vehicle.

New Car Websites

Used Car Websites

Step 2 (Cost of Gas):
Using the Federal Governments Fuel Economy Website, determine the annual fuel cost for your choices and record this information on the Datasheet Handout.

Step 3 (Cost of Insurance):
Using this website, determine the average annual insurance cost for both of your choices.  Skip the "Find Affordable Auto Insurance" section at the top of the page and scroll down to the sortable table.  If your choice isn't listed, use the cost for a similar model.  Record this information on the Datasheet Handout.

Step 4 (Create a Table):

  1. Your next task will be to use Excel to create a table of the total cost of ownership of both of your vehicles.  After opening Excel, start a table that looks similar to the one below.  You will need to change "Honda Accord" and "Toyota Camry" to the models that you chose.


2. Next, highlight the second and third row in the "Year" column and then drag the lower right-hand corner down until you reach the number 15.



3.  Enter the purchase price for both of your vehicles in the row for "Year 0".



4  Now you need to determine how much it costs to use this vehicle every year (which represents the slope).  Add the yearly fuel cost and yearly insurance cost to the purchase price for each vehicle and enter that value in the row for "Year 1".  In the example below, the yearly operating cost for the Accord is $1000 and the yearly operating cost for the Camry is $800.




5.  Highlight the first two rows for your first choice of vehicle.  Then, drag the lower right-hand corner down until you populate data for all 15 years.  Then repeat the process for your second choice of vehicle.  When doing this, Excel is using the slope to determine the total cost of ownership for each vehicle in all 15 years.





6. Print your table.

Step 5 (Create a Graph):

  1. Highlight the second and third columns of data in Excel and then click on "Insert" then click on "Line" and select the first line graph icon.


2. Excel should have produced a graph for you but we need to make some minor adjustments.  Right click somewhere in the graph and choose "Select Data".



3. Click on the "Edit" button under "Horizontal Axis (Category) Label".


4. Highlight years 0-15 and select "OK".  This will force Excel to change the labels on the bottom of the graph from 1-16 to 0-15.




5.  Use the "Layout" menu item in Excel to add a Chart Title, X Axis Title, and Y Axis Title.



7.  Print your graph.


Step 6 (Summary):
Answer all of the questions on the Summary Handout.

Step 7 (Turn in Project):
Staple the following documents (in this order) and hand in your project: (You will not be able to type into the forms....please copy and paste the forms in a word document)

  1. Summary
  2. Data Sheet
  3. Print outs that show price of both vehicles
  4. Excel Table
  5. Excel Graph


The following resources should be used to complete the task. All of these resources also appear in the Process section.


I hope you enjoyed shopping for a vehicle. You are now the proud owner of a vehicle your family will use on a daily basis.In the process of choosing a vehicle, you should have made good use of your algebra skills. Hopefully this exercise convinced you that the "when am I ever going to use this" question does have a valid answer. While you may not have gone through the exact same process in real life, many of the decisions you make in everyday life are some how related to algebra. 


Thanks to  Marc Kerschner(2001) Retrieved on January 31, 2011 from