Car Comparison Project
Introduction: Systems of linear equations are a useful way to solve common problems in different
areas of life. One of the most powerful ways to use them is in a comparison model where two similar
situations are compared side by side to determine which one is better. In this project, you will be
choosing two of the same model cars as listed below (the regular version vs. its hybrid version) and
then using systems of linear equations to decide which one is the better buy for you. Make sure that
each are that you are comparing is new and from the same year.
Regular Hybrids
1) Toyota Camry Toyota Camry Hybrid
2) Honda Accord Honda Accord Hybrid
3) Ford Fusion Ford Fusion Hybrid
4) Hyundai Sonata Hyundai Sonata Hybrid
5) Toyota Rav 4 Toyota Rav 4 Hybrid
Car Comparison
Situation: Your job requires you to be on the road a lot and therefore your company will buy you a
vehicle. However, in order to buy the vehicle, you need to demonstrate to your company that you
have researched your options and are purchasing the most economical vehicle you can. You are trying
to decide between getting a hybrid or a regular car. The hybrids cost more upfront, but get better gas
mileage, so it will cost less to drive. Regular cars cost less upfront, but get worse gas mileage, so they
will cost more to drive.
What information do you need to determine if a regular or hybrid car will be better?
Assignment: You will collect information from the internet (price and monthly gas cost) for each car
you chose. Then you will create a system of linear equations for the two cars. You will create a graph
and solve algebraically to determine which car will be the better buy for you. Make sure to NEATLY
show all your work. (Refer to the Rubric on Canvas for the point breakdown)
Project Steps
Step 1: Research the cars online. Name which set of cars you will be comparing.
Regular: Hybrid:
Give Make, Model and Style Give Make, Model and Style
Ford Fusion 2020 Ford Fusion Hybrid 2020
Cost ($) 23,170 28,000
Gas Mileage 21 MPG 43 MPG
(miles per gallon - city)
Step 2: Calculate what your monthly gas cost would be for each car. First, figure out how many gallons of gas you will
need to buy each month for each car.
a) Assume gas prices are $2.75 per gallon
b) You will be driving 1,500 miles per month
Regular: Hybrid:
Cost of Gas Each Month Show work here: Show work here:
1500/21= 71.4 gallons 1500/43= 35 gallons
71.4(2.75)= 196 gallon price 35(2.75)= 96 gallon price
Answer: $196 per month. Answer: $96 per month
Step 3: Create the linear equation for each car, letting x represent the number of months that you have driven the car
and y represent the total cost of the car to that month.
Regular: Hybrid:
Equation
y=196x+23,170 y=96x+28,000
Step 4: Use the equations you created in Step 3 to solve the system of linear equations by graphing using Geogebra.
a. Go to www.geogebra.org then click on “start graphing”
b. Type in both equations.
c. Label both equations by clicking on the 3 dots next to the equations, then click on “settings.” Under “Name” use
one word to describe which car corresponds to that equation (i.e. Accord or Hybrid)
d. On right side of the page click on the gear. Then click on “zoom to fit.” Optional: If you want to zoom it in a little
more from there you can using the mousepad or the magnifying glasses in bottom right.
e. Click on the gear again and then “settings.” On “basic” tab under axes click “bold”, on “x-axis” tab under label
type in “number of months”, on “y-axis” tab under label type in “Total Cost” and under units select the $.
f. Save a screen shot of what you just created. (make sure to include the equations, both axes, and point of
intersection) Paste Geogebra graph below.
At what point do the graphs intersect? (write as an ordered pair – Round each coordinate to nearest whole number)
My solution is: (48.3,32636.8)
Step 5: Solve this System of Equations by SUBSTITUTION. Show your work!!! Write answer as an ordered pair.
196x+23,170=96x+28,000
-96x -23,170 -96x -23,170
100x= 4830
100 100
x=483/10
x=48.3
y= 196(48.3)+23,170
y=32636.8
My Solution is: (48.3,32636.8)
Step 6: Solve this System of Equations by ADDITION/ELIMINATION. Show your work!!! Write answer as an ordered pair.
(-1)(-96x+y=28,000)(-1) 96x-y=-28,000
-196x+y=23,170 -196x+y=23,170
-100x= -4830
-100 -100
x= 48.3
y=196(48.3)+23170
y=32636.8
My Solution is: (48.3,32636.8)
Step 7: Reflection
a) Did you get the same answers on Step 4, Step 5 and Step 6? Should you get the same answers? Why or why not?
Yes, I got step 4,5 and 6 with the same answers because all of them have the same variables and information.
The only thing that changes is the method for finding those answers but the solution in all of the three steps is
the same.
b) It will take about 48 months (which is approximately 4 years) for the hybrid car to become the better deal
c) State which car (hybrid or regular) you would pick and why – remember that this is going to be a company car
and you are deciding for the company, so make sure to support your answer well.
Comparing the Hybrid and the Regular Ford Fusion is easy to find out that in terms of economy the Hybrid Ford
Fusion will make you safe a lot of money in the long run this is due to the Gas mileage (Miles per gallon-city).
Even though this car is $4,830 more expensive, it will start making you save money at some point which make it
more interesting for the economy of the person who decides to buy it.
