Solving Systems of Equations Simultaneously
Created by: Barbara Johnston, Lynn Scott, and Gary Kubina
Introduction Task Process Evaluation Conclusion Teacher Page
Introduction
Have you ever dreamed of owning your own car? Well, let’s take it to the next level. Consider owning your own car dealership! You’ll be making decisions about business practices such as investments and inventory. In this activity you will assume ownership of a car dealership. Start dreaming, but be sure to stay grounded in the mathematics.
Introduction Task Process Evaluation Conclusion Teacher Page
Task
Your group is going to create an advertisement in the form of a poster or a PowerPoint. You will write original problems based on your own dealership. Your problems should be modeled after the problems on the pre-activity worksheet.
All aboard!
You’re on your way!
Introduction Task Process Evaluation Conclusion Teacher Page
Process
· Review solving
systems of equations graphically by visiting this website: http://regentsprep.org/Regents/math/syslin/GrSys.htm
· Review solving
systems of equations algebraically by the addition or subtraction method. http://regentsprep.org/Regents/math/syslin/AlgSysAdd.htm
· Review solving
systems of equations algebraically by the substitution method.
http://regentsprep.org/Regents/math/syslin/AlgSys.htm
· Complete the
pre-activity/student worksheet Part I.
· Get into
groups of 3.
· Design your
own business using the pre-activity as your model/student worksheet Part II.
· Create a
PowerPoint presentation or a poster. See
worksheet Part III.
Introduction Task Process Evaluation Conclusion Teacher Page
Evaluation
|
Introduction Task Process Evaluation Conclusion Teacher Page
Conclusion
Systems
of equations can be used for solving many real world problems. You have discovered this by creating an
inventory for your own car dealership.
Congratulations. You’ve crossed the “finish line!”
Back to Student Page
Introduction Task Process Evaluation Conclusion Teacher Page
Teacher
Page
Subject Area: Math
Grade Level: 9-11
Learner Information:
This WebQuest was written for Algebra I students, but can be
modified for use with Algebra II students. This is a closure activity for
the chapter on solving systems of linear equations.
For successful
implementation of this WebQuest , students should:
- know how to use the
Internet.
- know how to use Microsoft
Power Point (optional).
Standards:
Curriculum:
Algebra I/Standard # 8: Solve systems of linear equations and
inequalities in two variables graphically and algebraically.
· Modeling
real-world problems by developing and solving systems of linear equations and
inequalities.
Technology:
29. Apply
appropriate techniques for producing multimedia products.
33.
Demonstrate proficiency in presenting digital information.
34. Use
appropriate on-line resources for research.
Student Worksheet:
Using Systems of Equations in Business
A
local car dealership carries an inventory that includes cars and trucks. A system of linear equations can be used to
track the inventory. Use the information
given to write and solve a system of two equations in two variables to solve
each problem.
First
briefly describe how to use each of this method of solving a system of linear
equations:
1.graphing:
2.substitution:
3.elimination by
addition or subtraction:
4.elimination
with multiplication:
Given
the information for the following situation, select the most efficient method
to write and solve a system of equations.
Explain why you used the selected method.
5.On Monday the
ABC car dealership takes inventory. The
current inventory includes cars and trucks. The average price for a car on the
lot is $19,500 and the average price for a truck is $24,700. If the total value of inventory is equal to
$2,168,400 at this time, write an equation that represents the value of the
inventory. Choose and define a variable
to represent the number of trucks and choose a second variable to represent the
number of cars.
6.The sales
manager counts the number of vehicles on the lot and finds that there are a
total of 100 vehicles. Write an equation
that describes the number of trucks and cars that are on the lot.
7.Use the two
equations from 5 and 6 to calculate the number of trucks
and cars that are currently on
the lot.
8.Which method
of solving systems of equations did you use?
Why?
9.If two trucks
and three cars were sold on Monday, what would be the total value of the
inventory on Tuesday?
10.
On Tuesday afternoon a shipment of four trucks is
delivered. What is the new value of the
inventory?
Return to Process.
Design
your own company and use systems of equations to help you decide on your
inventory. Use actual prices that you
can find by using newspaper ads, by searching Internet sites, or by contacting
local car dealers. Begin by deciding on
the total value of inventory (dollars) that you will have on your car lot. Then decide how many of each model of car or
truck you will keep in inventory. Select
only two models or categories of vehicle.
Decide the average price of each model.
Generate and solve equations for your inventory.
Using
the pre-activity questions as your guide, write questions related to your
inventory.
Write
up all questions on one sheet of paper and answers on a separate sheet.
Total
dollar value:
Total
number of vehicles:
Describe
your car lot situation and explain how you used systems of equations to help
make decisions about your inventory.
Return to Process.
Your
group will design a poster or PowerPoint advertisement for your business. Decide on an original name for your
business. Your advertisement should be
eye catching and accurately state information about your products (cars and
trucks). Include illustrations of the
cars and trucks that you will have on your car lot. Clearly label the names and prices of each
vehicle.
Return to Process.
