Name:
Algebra 1—Car Comparison Project
Period:
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 cars that you are interested in purchasing and then using systems of linear
equations to decide which one is the better buy for you.
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 vehicle.
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.
For this project, you will need to choose one hybrid vehicle and one non-hybrid vehicle.
Assignment: You will collect information (price and monthly gas cost) for each car you chose. Then you will create a system of
linear equations for the two vehicles and create a graph to determine which vehicle will be the better buy for you.
You will be completing and turning in this packet as well as a poster as your final products for the project.
Step 1: Research your cars online.
Hybrid
Type of Car:
Non-Hybrid
Type of Car:
Cost ($)
 Round to the nearest 1,000
Gas Mileage (miles/gallon)
Step 2: Calculate what your monthly gas costs would be for each car. In order to do this, please assume the following…
 Gas costs $3.00 per gallon
 You will be driving 1000 miles per month
 Hint: First, figure out how many gallons of gas you will need to buy each month for each car.
Hybrid
Type of Car:
Non-Hybrid
Type of Car:
Work:
Work:
Answer:
Answer:
Monthly Gas Costs
Step 3: Create the linear equation for each car. Let x represent the number of months you drive the car and y represent the total
cost of the car.
Hybrid
Type of Car:
Equation
Non-Hybrid
Type of Car:
BEFORE YOU MOVE ANY FURTHER…
Have your teacher check your equations and initial on the line.
Step 4: Solve the system of linear equations both graphically (by method of graphing) and algebraically (by method of substitution
and elimination).
Solution by Graphing:
My Solution is…
(
,
)
Solution by Substitution:
My Solution is…
(
,
)
Solution by Elimination:
My Solution is…
(
,
)
Step 5: Create a poster that shows the comparison between the two cars. Your goal is to successfully explain and represent which
car is the better buy.
Your poster MUST include the following:
1. A table that shows…
a. Price of each car
b. Gas mileage of each car
c. Total monthly gas costs for each car
d. Equation for each car
2. Work shown for your solutions using the following methods…
a. Graphing
b. Substitution
c. Elimination
3. An explanation for which car you will be choosing. This explanation must be 4-6 sentences long.
4. Name and Period on the back of the poster.
Although this is not the required format, here is an idea of how your poster can be organized. Still, feel free to be creative! 
CATEGORY
Research,
Equations, and
Tables
Graphing
Method
Substitution
Method
Elimination
Method
Writing
Component
EXCELLENT
Average
Below-Average
Poor
4 points
Research is done in
advance, equations
and tables are 100%
correct.
3 points
Research is done in
advance, equations
and tables include
minimal flaws.
2 points
Research is done in
advance, equations
and tables have
multiple flaws
1 point
Research is not done
in advance and/or
section is incomplete.
Equations are
correctly graphed,
solution is identified
correctly.
Equations are
correctly graphed,
but solution is
incorrect.
OR
Exactly 1 equation is
not graphed
correctly, but
solution makes sense.
Substitution is used.
Minor flaws in work.
Work is checked.
OR
Substitution is used.
Answer is correct.
Work is not checked.
Elimination is used.
Minor flaws in work.
Work is checked.
OR
Elimination is used.
Answer is correct.
Work is not checked.
Conclusions are
drawn and methods
are analyzed with
minimal flaws.
AND
Minimum length
requirements are
met.
Both Equations have
minor flaws, but a
sensible solution is
given.
Both equations have
flaws, and solution is
not sensible.
Substitution is used.
Minor flaws in work.
Work is not checked.
Substitution is used.
Major flaws in work.
Elimination is used.
Minor flaws in work.
Work is not checked.
Elimination is used.
Major flaws in work.
Conclusions are
partially incorrect
and/or methods are
analyzed with some
flaws.
AND
Minimum length
requirements are
met.
No relevant
conclusions are
drawn and the
methods are
incorrectly analyzed.
AND/OR
Minimum length
requirements are not
met.
Substitution is used.
Answer is correct.
Work is checked.
Elimination is used.
Answer is correct.
Work is checked.
Accurate conclusions
are drawn and
methods are properly
analyzed.
AND
Minimum length
requirements are met
Comments:
Total:
/ 20 points