ERIE COMMUNITY COLLEGE
TITLE III
Linear Equations
Interdisciplinary Course Materials
Office Management
Course: MT013 and MT007
Course Outline Topic: Writing and evaluating linear equations with applications, graphing linear equations, slope of a line, and solving and interpreting the graph of two equations in two unknowns
Project Title: Comparing earnings of part-time jobs (Waitress vs. Cell Phone Salesperson)
Project description: Students will be asked to write equations that will be used to compute the earnings of a waitress/waiter and a cell phone salesperson based on sales given different hourly rates and different rates for tips or commission. They will then be asked to plot the earnings on a graph and analyze the data to determine which job would be their best choice. Students should determine which job would generate the greatest amount of income for different ranges of sales.
Author: Janet Evert
Curriculum Expert: Susan Ballard
Semester Created: Fall 2007
A. Essential Question
What are the potential earnings for two different jobs – the waiter/waitress versus a cell phone salesperson? Which position has the greatest potential for earnings? Which could end up with the least amount of earnings? What would be the projected wages for each job based on a realistic amount of sales? Which job would be the best choice?
B. Introduction
Assume that you are looking for a new job and are considering two different job offers, both based on sales. The first job is working as a waitress/waiter and the other job is working as a salesperson for a local cell phone company.
You will use your knowledge of writing, evaluating and interpreting linear equations, and graphing and solving two equations in two unknowns to calculate the earnings potential of each job. This analysis will help you to decide which job you should take.
C. Basic Directions
You will first write a linear equation that can be used to predict the wages for
each job based on the amount of sales for a wide range of values. You will then compile the results in table form and plot the resulting points on a graph. Using what you know about two equations in two unknowns will allow you to analyze the results and decide which job would work best for you.
D. Things to Learn Before Starting the Project
1. Know how to write and evaluate linear equations.
2. Know how to create a graph and plot points using a linear equation for a real-life situation.
3. Understand how to interpret the graph to predict values.
4. Understand the concept of two equations in two unknowns and interpret the results.
E. The Project Assignment
You are looking for a part-time job while you attend ECC. You have been offered two different jobs—a waiter/waitress position and a cell phone salesperson.
Part I – Write the Equations and Determine Potential Earnings
1. The waiter/waitress position pays $4.65 per hour but also produces tips based on the total tab for the tables that you served. In talking to other servers, you know that customers, on average, leave around a 14 percent tip; on any given evening, you would expect tabs to bring in anywhere between $300 and $900 in total receipts for a four-hour shift.
a. Write an equation that would describe the earnings that you would get for one four-hour evening shift working as a waiter/waitress. Use W for wages and S for the total sales in tabs for the day.
b. Calculate the potential earnings based on sales
S (sales) / W ( wages)from $0 to $1,400 and enter the results in the table given.
c. An increase of $100 in tabs (sales) would result in an increase of how much in wages. Write the answer as a slope: the rate of change in input with respect to the rate of change of output.
2. The second position you are considering is that of a cell phone salesperson. This position pays $10 an hour with a 7 percent commission on the sales of all plans.
a. Write an equation that would describe the earnings that you would get for one four-hour evening shift working as a cell phone salesperson. Use W for wages and S for the total sales for the day.
b. Calculate the potential earnings based on sales
S (sales) / W ( wages)from $0 to $1,400 and enter the results in the table given.
c. An increase of $100 in sales would result in an increase of how much in wages for this job? Write the answer as a rate of change or slope.
Part II – Create a Graph
1. Determine which value, Sales or Wages, is the input value and which one is the output value for this problem. The input value is normally graphed along the horizontal axis. The input value is typically the one that you would put into the equation to predict the output value. The output value is normally graphed on the vertical axes. Use S for dollar amount of Sales and W for dollar amount of sales.
2. Choose an appropriate scale for both Sales and Wages and label the graph clearly.
3. Using the results found and listed in the table of values found for the Waitress/Waiter earnings, plot the results as points on the graph. Draw a line by connecting the points. Do these points give you a straight line? If not, go back and check the results in the table.
4. Using the results found and listed in the table of values found for the Cell Phone Salesperson earnings, plot the results as points on the same graph. Draw a line by connecting the points. Do these points give you a straight line? If not, go back and check the results in the table.
Part III – Analyze the Results
1. What do you think a realistic amount of sales would be for a four hour time period for a waitress/waiter and for a cell phone salesperson. Do some investigating if you do not know. Be sure to come up with a realistic range of sales for each job.
2. Look at the graph to see if you could find the potential realistic range of earnings for each job. Which job would have the greatest potential for earnings?
3. For what range of sales would the waitress job pay more than the cell phone salesperson? For what range of values would the cell phone salesperson’s job pay more than the waiter/waitress position?
4. Look at the graph to and see if you can determine what amount of sales would result in the same salary for both jobs? Approximate the answer.
5. Using your knowledge of two equations in two unknowns, solve the system of two linear equations in two unknowns algebraically to find what amount of sales would result in the same salary for both jobs? This will produce an exact answer.
F. Student Resources (websites, books, technology, etc.)
Students should refer to the chapters on Writing Linear Equations, on Graphing Linear Equations, and on Two Equations in Two Unknowns. In the current text, Elementary Algebra for College Students (7th edition) by Alan Angel, that would include Chapters three, seven, and eight.
Calculators should be used for this project.
G. Faculty Resources (teacher notes, websites, books, technology, etc.)
This would make a good group project as students would need to discuss the best choices and the reasoning involved in making their decisions. This works especially well for choosing the proper scales for graphing the problem initially and for choosing what values to use for potential sales for each job.
This project also provides an opportunity to discuss the fact that the linear relationship of the wages earned based on dollar amount of sales may hold true for only a certain range of sales.
This project could be expanded to have students look at how each of these jobs might compare to a straight salary job such as working at Taco Bell for $8.00 per hour.
H. Grading Rubric
Part I Write the Equations and Determine Potential Earnings 50%
Part II Create a Graph 30%
Part III Analyze the Results 20%
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Erie Community College
Title III Grant