Reference no: EM131267344

Introduction:

Individuals encounter countless situations in day-to-day life that require a strong mathematical foundation in order to make informed decisions.

Shown below are four real-world scenarios that one might encounter in day-to-day life.

For this task you will choose one of the scenarios below. Each situation requires a mathematical comparison of cost options in order to determine which is best for a consumer (e.g., customer or person).

Scenario 1:

A parent is looking for the best option for daycare for a child. A home-based option charges a flat rate per hour. A center-based option charges a fixed fee per week for a certain number of hours and then a fixed rate per hour for any hour provided over the set amount. Determine which option is most advantageous for the parent based upon the parents' needs.

Scenario 2:

A downtown employee is looking for the best option for parking a car during a 5 day work week. One parking garage offers unlimited parking at a flat rate per month. Another garage offers an hourly rate for parking. Which option is best for the employee on a monthly basis?

Scenario 3:

A family is looking for the best option for moving the family's belongings into a new home. Moving company A charges its customers a flat rate per mile. Moving company B charges its customers a fixed amount for a certain number of miles and then a fixed rate per mile for any miles over the set amount. Determine which company would best serve the needs of the family.

Scenario 4:

A student is looking to secure a hardcopy textbook for an upcoming course. Compare a weekly textbook rental option with a purchase option to determine which option is most advantageous for the student based upon the student's needs.

Task:

Note: Part A, B, and D of this task should be completed in a word-processing program; hand-written artifacts are not acceptable for this task. Part C should be completed in approved graphing software; hand-drawn graphs and graphs crafted as art within a computer program are not acceptable for this task.

A. Develop a story problem using the real-world scenario you have selected from the four provided above by doing the following:

1. Develop a cost comparison problem that can be solved according to the task instructions that follow by supplementing your chosen scenario with additional information.

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, within a spreadsheet application using integrated graphing tools (e.g., Microsoft Excel, OpenOffice Calc, LibreOffice Calc).

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.
- Save and submit your spreadsheet as an *.xls, *.xlsx, or *.ods file.

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.

E. When you use sources, include all in-text citations and references in APA format.

Note: When bulleted points are present in the task prompt, the level of detail or support called for in the rubric refers to those bulleted points.

Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link included in the Evaluation Procedures section.

Note: When using sources to support ideas and elements in a paper or project, the submission MUST include APA formatted in-text citations with a corresponding reference list for any direct quotes or paraphrasing. It is not necessary to list sources that were consulted if they have not been quoted or paraphrased in the text of the paper or project.

Note: No more than a combined total of 30% of a submission can be directly quoted or closely paraphrased from sources, even if cited correctly. For tips on using APA style, please refer to the APA Handout web link included in the General Instructions section.