Shopping for a Cellular Plan Using Systems of Equations

It’s your money What do spend your money on? –G–Gas –F–Food –I–Insurance –C–Cell Phone –H–Hot Dates

When you earn your paycheck you want to make sure that you earn more then you spend. As you get older you gain more financial responsibilities. Algebra can help! Tools to spend your money wisely.

How much do you pay? Do you know how much you or your parents pay for your cell phone plan? How many minutes do you get each month? How much do you pay if you go over your minutes?

Quick Review When two linear equations intersect you have an ordered pair. This ordered pair is the solution for the Systems of Equations. You can graph the two equations and see where they intersect.

Quick Review The equations x + y = 24 and 3x + y = 44 together are called a System of Equations One method for solving a system of equations is to carefully graph the equations on the same coordinate plane. The coordinates of the point at which the graphs intersect is the solution of the system.

Quick Review (-2,2)

Quick Review You can also use Substitution or Elimination to find the solution without graphing.

Example… Option 1: Redcom offers a monthly payment of $15 for 300 minutes, an activation charge of $5 and an additional charge of 75 cents per additional minute. Option 2: BlueGrill Wireless offers a monthly payment of $45 for 300 minutes, an activation charge of $15 and an additional charge of 50 cents per minute. Which is the more economical offer?

Step 1: Construct a table Additional Minutes Cost at RedCom Cost at BlueGrill (30) (30) + 60

Step 1: Construct a table Number of Minutes Cost at RedCom Cost at BlueGrill $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

Examine your table... What patterns do you observe from the table of values? What happens to the cost of the cell plans as the number of minutes increases? What would a graph of this relationship look like? Which company offers the best deal? Is there a point where the two cell providers charge the same amount? If so, what is the charge? If not, why do the costs never equal?

Step 2: Write the algebraic rules From the description of the two offers, write an algebraic rule that will determine the cost of "x" minutes from each of the two dealers: RedCom f(x) = ________ BlueGrill g(x) = ________

Step 2: Write the algebraic rules From the description of the two offers, write an algebraic rule that will determine the cost of "x" minutes from each of the two dealers: RedCom f(x) =.75x + 20 BlueGrill g(x) =.50x + 60

Step 3: Make a graph Now use Excel to graph the two sets of data using a line chart. Now use your graphing calculator to graph the two cost functions and see if the values match the Excel values. Arrange your window so that you can see where the linear functions cross. Use the intersection function on your calculator to see where the two functions cross.

Step 4: Analyze your data What effect does the 75 cents per minute cost have on the graph of the RedCom function? What effect does the $20 have on the graph? What effect does the 50 cents per minute cost have on the graph of BlueGrill function? What effect does the $60 have on the graph? Which cellular dealer offers the best deal? What are the coordinates of the point where the two functions intersect? What is the significance of this point?

Step 4: Analyze your data Intersection (160, 140)

Questions to be answered Based on the data in the table and the graph above, what cellular provider might you choose? Which provider has is the best deal? What other information would you need to consider before making your decision?

Questions to be answered What effect does the monthly payment have on the graph? What effect does the additional cost per minute have on the graph? What are the coordinates of the point where the two functions intersect? What is the significance of this point?

The Product You will need one plan from each carrier that are comparable. Then you will create a table using Excel comparing the total cost between the two plans for n number of minutes. Using that table you will create a line graph in Excel.

The Product You are employed by a consumer advocate organization and they want you to create a brochure comparing wireless plans. You are to go online and research two cell phone plans.

The Product In your brochure you must include the table, graph, equations, and answer the questions on the slides titled ‘Questions to be answered’. You will need to cite your sources on the brochure. Make the brochure visually appealing. The front of the brochure should be eye catching.