Appendix E
Extending the scenario to include combinations of uniform types leads to the mathematical development of writing, solving, and graphing linear equations and inequalities with two variables.
Two Variable Equation Example
The company selling uniforms allows us to buy two types of uniforms. Some athletes like the Decent uniforms while others like the Name Brand uniforms. A Decent uniform costs $24 and a Decent uniform costs $32. Ms. Gonzalez and Mr. Delgado adjust their estimate of uniforms that we need to buy to be at least 350 uniforms with the $10,000.
Example Questions
The primary question for this situation: Will we be within our budget if we wanted to buy Decent and Name Brand uniform types for a total of 350 students?
The following questions are some of the questions that can be used as scaffolds to assist students with answering the primary question.
What is the least amount we should plan on spending?
What is the most amount of money we should plan on spending?
How many uniforms could we buy if we choose only the Decent uniform type?
How many uniforms could we buy if we choose only the Name Brand uniform type?
How much would it cost if we chose 100 Name Brand uniforms and 250 Decent uniforms with the deal?
If we wanted at least 200 Name Brand uniforms, would we have enough money to buy Name Brand uniforms for the remaining number of students?
If we wanted 350 uniforms total, are there at least 3 combinations of Decent and Name Brand uniforms that would be below budget based on the funding constraint? Justify your answer.
Can you find any combinations of Decent and Name Brand uniforms that would be just right for the budget, making sure that every dollar is spent? Justify your answer.
By using different combinations of uniform brand types, varying the quantities, and varying the prices, this context can be a starting point towards discussions on two-variable equations and inequalities and an introduction to systems of linear equations.
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