This activity focuses on analyzing supply-and-demand problems from
business by solving systems of equations and finding the equations for
It is assumed that students are familiar with:
- How to find a linear equation from a graph from 2 points or from the slope and the y‑intercept
- How to solve systems of 2 equations in 2 unknowns.
You may wish to acquaint students with the following concepts from economics at the beginning of the activity session.
- Supply can be defined as the quantity of the item that is in stock.
is a factor in the supply of an item. When the price of an item is low,
more people buy the item, and the supply (stock on the shelves)
decreases. When the price of an item is high, the supply remains high
because fewer people buy the item, leaving more inventory on the
Supply vs. Demand
- Demand can be defined as the quantity of merchandise the consuming public wishes to buy.
affects demand. A lower price tends to increase the demand because
people may feel that the item is a bargain, while a higher price tends
to decrease the demand.
supply is greater than demand, the merchant suffers. The merchant has a
stockpile of merchandise that is not making any money for the business.
- When demand is greater than supply, the merchant
also suffers. Customers are coming to buy an item that may be sold out,
and an opportunity to make a sale is missed.
- The merchant is best served when supply and demand are in equilibrium.
Equilibrium occurs when the price is set so that the supply and demand
equal each other. The item completely sells out, but no one who wants
to purchase the item goes home without it.
Graphing Supply and Demand Against the Price
Once students have an idea of how the price of an item can
affect sales, they have a context in which to understand the graphs
offered on the following activity sheets.
Activity: Class Fundraiser
Having a transparency of Activity Sheet: Senior Class Buttons makes it
easier for you to guide students into a discussion about supply and
Students may not initially recognize what to do with 3 columns of data.
Question 1: Coach students to use the price column for x‑values and the 'supply' column for y‑values.
Question 2: Coach students to use the price column for x‑values and the demand column for y‑values.
Allow sufficient time for students to plot points and complete the
graphs. If possible, check students' graphs. Students can work
individually or in pairs to answer Questions 3–8. Point out that they
have used 3 different ways to display and interpret the information
given in this button example. The data were presented to them in a table. They used the data to construct a graph that allowed them to understand more about the problem. Then they wrote and solved a system of equations that represented the same information in yet another form.
Activity: Game Cartridges and Silver Dollars
Game Cartridges and Silver Dollars
The 2 scenarios on this activity sheet can be assigned for homework or used as additional class activities.
After working through the button example from Activity Sheet 1 and the
game cartridge example on Activity Sheet 2, students may get too
comfortable with values that predict a straight line. Point out to
students that this result rarely occurs in real-world situations.
The second problem on Activity Sheet 2, about silver
dollars, is a good example of realistic data. Even though the supply-and-demand functions
are not linear and no formulas are given to represent the functions,
students can draw conclusions when they study and interpret the graphs.
Point out to students that many times a line or a formula is used that
is a good approximation based on the given data.
By the end of this lesson, students will:
- Explain factors that affect supply and demand.
- Find linear equations for given sets of supply and demand data.
- Find the equilibrium point for a system of supply and demand equations.
- Translate between table, graph, and equation representations for supply and demand data.
NCTM Standards and Expectations
- Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases.
- Use symbolic algebra to represent and explain mathematical relationships.
- Draw reasonable conclusions about a situation being modeled.