A. Create a story problem using one of the above real-world scenarios 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. 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 (e.g., Excel). Note: For this task, your graph must be computer-generated rather than drawn by hand on graphing paper or crafted as art within a computer program. Spreadsheet applications, such as Microsoft Excel and OpenOffice Calc, are highly recommended for this activity. If you do not already have access to a graphing application, or if you do not know how to use the graphing application you have access to, please visit the QLT1 Course of Study and consult with a QLT1 course mentor. Include the following details in your graphical representation of the real-world problem:

• Label each axis of the coordinate plane with descriptive labels.

• Label all graphical solution(s) of the system of equations as “solution” and include the ordered pair.

• In a legend, indicate which cost option corresponds with each line.

D. Discuss a decision-making process that is based on both mathematical reasoning and non-financial, or situational, considerations. Your discussion should include the following:

• How financial information gleaned from your algebraic and graphical analyses can be used to determine the conditions for choosing cost option A over cost option B and vice versa

• How non-financial, or situational, considerations can impact the decision-making process

1. Discuss a final recommendation that states the option that most closely meets the consumer’s financial needs and non-financial considerations.

Compare a yearly pass with a daily pass at a health club, zoo, museum, or theme park to determine which option is most advantageous for a customer based upon the customer’s needs. Parts A1-A3 A family is getting ready for summer as the school year ends. The family knows they want to go to the nearby amusement park several times this summer. Both of the children are old enough to go on the rides and their parents are both teachers, they will not be working. The family thinks that they will go to the amusement park 3 times each month during break, the family has June, July, and August off. The family wants to find out if they should get summer passes to the amusement park or if they should buy day passes each time they want to go to the park. The family has a budget on how much they want to spend throughout the summer at the amusement park. The family would like to stay close to 1200$ for their family of four to attend the amusement park during the summer months. The following is two options that the family can consider: Plan A: daily passes for the amusement park are as follows: -Ages 3 to 18 are $25.00 per day -Ages 18 and up is $40.00 per day The family would need two children’s tickets and two adult tickets per day Plan B: A summer season pass at the amusement park is as follows: -All ages 3 and above $140.00

A. Introduce the problem by doing the following:

1. Describe the selected real world scenario.

2. Explain the needs of the hypothetical customer.

3. Discuss two cost options that are being considered.

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

1. Develop a linear algebraic equation with clearly defined variables to represent the cost of each option.

2. Explain the reasoning behind the way each equation is constructed.

3. Solve the system of linear equations algebraically using either the substitution method or the elimination method to determine where the two cost options are equivalent, showing all work.

Explain each step used to solve the system of linear equations. Include the following in your explanation: *The algebraic method used to solve the system of equations. *All mathematical operations used to solve the system of equations. *The solution of the system of equations.

C. Depict the situation graphically. Include: a depiction of each cost option on the same graph, clear labels of the cost to the hypothetical customer for both options on the graph, the intersection of the cost options (if one exists)

D. Discuss a decision-making process that is based on both mathematical reasoning and non-financial, or situational considerations. Your discussion should include the following: How financial information gleaned from your algebraic and graphical analyses can be used to determine the conditions for choosing cost option A over cost option B and vice versa. How non-financial, or situational considerations can impact the decision making process.

1. Discuss a final recommendation that states the option that most closely meets the consumers financial needs and non-financial considerations.