Introduction Systems of linear equations are a useful way to

Introduction Systems of linear equations are a useful way to solve common problems in different areas of life. One of the most powerful ways to use them is in a comparison model where two similar situations are compared side by side to determine which one is better. In this project, you will discuss a real life situation and then use systems of linear equations to decide what to buy. The two situations are: Cell phone plans, comparing monthly fee and price per text message. Assignment: Gather information from Verizon and AT&T; in the following catalogue. Then write a system of linear equations for the two plans and create a graph. Use the methods we have been studying to determine which plan is better based on the number of text messages you send per month. Project Details Collect the data from the catalogue. Write the system of linear equations and a word problem once the data has been collected. Use both methods we have been studying (graphing and solving algebraically) to find the solution to the written system. When you graph the system of equations, be sure to create an appropriate scale on your x-axis and y-axis. Label the graph accordingly. Design the final display of the project on construction paper. Complete the questions on this handout. Complete the following questions: Which cell phone carrier is the better buy if you send 75 text messages for the month? Based on the number of text messages you send a month, which cell phone carrier is the best buy for your iPhone? How many months will it take for the cell phone carriers to cost the same amount of money? What does this number represent? At this rate of text messages that you can send in which both carriers would cost the same amount, what is the final cost of the plan? What does this number of text messages you can send at a specific cost for both carriers represent? Can you think of another real life situation where systems of equations would be beneficial? How would you this situation improve your insight and further your knowledge?

Solution

Answer of question (1)

HEre total cost = fixed cost + variable cost= fixed cost + rate of one message x total messges

so total cost of verizon wireless= 22 + 75(0.5) =22+37.5 = $59.5

And accordingly total cost of AT&T = 37+75(0.35) = 37 + 26.25 = $63.25

So clearly as the total cost of verizon wireless is less, this phone should be the best choice.

Answer