This activity focuses on solving systems of equations and finding the equations for lines to analyze supply-and-demand problems from business.
Prerequisites:
These activities assume that students are familiar with procedures used to find a linear equation given two points or the slope and the y-intercept. Students are also expected to know how to solve systems of two equations in two unknowns.
Important Concepts:
The teacher may wish to acquaint students with the following concepts at the beginning of the activity session.
The quantity of merchandise that a merchant has available to sell is called the supply. The supply may be affected by storage space, speed of manufacture, or general availability of a product from the merchant's supplier. Increasing the price of a product tends to increase the supply. The more expensive the product is to the consumer, the more willing manufacturers are to
produce it. An increased price may slow the consumption of the product and thus also increase supply.
The quantity of merchandise that consumers wish to buy is called the demand. Price also affects demand. A lower price tends to increase the demand, and a higher price tends to decrease the demand.
When supply is greater than demand, the merchant suffers. The merchant has a stockpile of merchandise in which the customers are not interested. The merchant's inventory is up, storage space is being used, and merchandise is not selling. When demand is greater than supply, the merchant may also suffer. The customers are willing to buy; however, the merchant cannot furnish enough
merchandise for them. The merchant may lose customers and consequently lose sales.
The merchant is best served when supply and demand are in equilibrium. This situation occurs when a price is found that makes supply and demand equal each other.
Distribute the Supply and Demand Activity Sheets to students. Follow the specific instructions below for each of the three Parts of the activity sheets. Students may wish to use additional grid paper, as needed.
Part I: Burgerama Cartoon Dolls
A transparency of the first sheet makes it easier for the teacher to guide students into a discussion about supply and demand. Make sure that students have the correct graph before they begin work on the next part of the activity sheet.
Part II: Video Games
Students can work individually or in pairs to answer the questions on this part of the activity sheet.
Point out to students that they have used three different ways to display, use, and discuss the information given in Part I: Burgerama Cartoon Dolls. The data were presented to them in a table. They used these data to construct a graph that allowed them to understand more about the problem. Then they used algebraic methods to find and solve a system of equations that represented the same information in a different form. (Students could use the equations that they get in Part II to determine the accuracy of their estimates from the graph.)
Part III: Silver Dollars
After working on Parts I and II, students may begin to wonder if they will always get a straight line when they
plot their points. Point out to students that in real-world applications this result rarely occurs; Part III is a good example.
Even though the supply-and-demand functions are not linear and formulas are not given that represent the functions, students can draw conclusions when they study and interpret 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.
