Mathematical Reasoning

A student is looking for the best option in purchasing school supplies. Company X is offering a 8% discount for every dollar amount spent; Company Y is offering a 18% discount, but the discount is applicable only when the dollar amount spent is above $150. Determine which company is more advantageous based upon the student’s needs. 

Task: A. Create a story problem using the above real-world scenario as a basis, including realistic numeric values, by doing the following: 

1. Describe the real-world problem. 

2. Explain all needs (e.g., financial, non-financial, situational) of the hypothetical consumer. 

3. A. Discuss two cost options that are being considered. 

B. Analyze the cost of each option algebraically by doing the following: 

1. Develop an algebraic equation(s) with clearly defined variables to represent the cost of each option. Note: In some circumstances, a single cost option may require two equations 

2. Explain the reasoning process used to translate the written description of each cost option into algebraic equations. 

3. Solve the system of equations algebraically to determine where the two cost options are equivalent, showing all work.

a. Explain each step used to solve the system of equations. Include the following in your explanation:

• All mathematical operations used to solve the system of equations

• The solution(s) of the system of equations in ordered-pair notation 

C. Depict the real-world problem on a single graph, using appropriate graphing software.

D. Discuss your recommendation to the customer based on both mathematical reasoning and contextual details. Your discussion should include the following:

• How the algebraic evaluation and graph support the recommendation

• Any relevant contextual details that pertain to the recommendation (e.g., flexibility, distance, availability, etc.)

1. Discuss the different options and the customer’s needs. Discussion (using graph)