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
ofeach 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, OpenOfficeCalc, LibreOfficeCalc).
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 *.odsfile.
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.
Task 5
Scenario 4:
A student is looking to secure a hardcopy textbook for an upcoming course. Compare a weekly textbook rental option to determine which option is most advantageous for the student based upon the student’s needs
A.
1. A bookstore offers rental and purchase options. If the customer chooses to rent a book, the book would be allowed for viewing for the extent chosen or the extent of the course being taken. Once the end of course date is complete, the book will need to be returned. If the purchase option is chosen, upon payment the course manual will be handed to the customer without expectation on return. If the customer needs to use the text for an extended amount of time, buying the book to own will be the best option. If the customer will use the text for brief viewing, renting will be a cheaper option.
2. Acustomerrequires a textbook to study for a 12 week course. The customeris taking a full time academic load but still thinks they will have enough time to complete the readings and course work quicker than expected. The customer thinks that9 weekswill be all the time they need and will have to figure out if renting or buying is the better deal.
3. The cost to own the textbook is $128 or the cost to rent the textbook for an allotted timeframe is only $16.
B.
1. Purchase Price: y = $128
Rental Price: y = $16x
Y represents the total price for renting the textbookor purchasing of thetext. X represents the number of weeks the book is rented.
2. The rental rate equation uses a weekly rate of $16 and X as the possible number of weeks the consumer will rent the textbook. Based on this equation the customer will be able to determine rental costs on the estimated time needed and compare it to the price of buying the text outright for unlimited usage but a possible higher rate.
3.Purchase
· y = 128
Rental
· y = 16x
To determine where the cost options are equivalent I will substitute the first equation into the second equation.
128 = 16x
128/16 = 16x/16
8 = x
The equationproves that renting the book for 8 weeks is equal to purchasing the book
· x = 8, y = 128
· order pair= (8,128).
C.
D. The customer hopes to finish a 12 week course in 9 weeks. To rent the book for 9 weeks would be $144. The buy the textbook outright would be $128, which is $16 less than renting the book making buying the book a better deal. The only way renting the book would be a better deal is if the customer could complete the course in 7 or less weeks. If the customer chose to rent the book for the 9 week period they were hoping to complete the course in, they would be paying more than the book is worth. At 8 weeks is where the renting and buying prices break even and the customer would need to choose the value of possessing the textbook verses borrowing it since the financial values are equal.
