Question

12. Carly's family is going to buy cell phones for the entire family. After some research they have narrowed their choices

down to 2 companies. AT&T charges a monthly rate of $100 plus $15 for each phone on the account. Their competitor,
Sprint, charges a flat monthly fee of $200 and they will receive an unlimited number of phones on the account.
a. Write an equation for the cost of each cell phone provider and then graph the equations.
AT&T:
Sprint:
b. Use any method to determine which company would be cheaper if Carly's family consists of Carly, mom, dad, two brothers, and one sister. Explain your reasoning

Answer 1

Explanation:

a. The equation for the cost of AT&T would be $100 + $15n, where n is the number of phones on the account. The equation for the cost of Sprint would be $200.

We can graph these equations on a coordinate plane with the x-axis representing the number of phones on the account and the y-axis representing the monthly cost. The graph for the cost of AT&T would be a straight line starting at the point (0,100) and going through the point (1,115), (2,130), etc. The graph for the cost of Sprint would be a horizontal line at the y-coordinate of 200.

b. In order to determine which company would be cheaper for Carly's family, we can simply plug in the number of phones they have (5) into each of the equations we derived in part a. This would give us a cost of $200 for AT&T and $200 for Sprint. In this case, both companies would be equally cheap for Carly's family.

Alternatively, we could graph the equations and see which company's line is lower on the y-axis for the given number of phones (5). This would also show that both companies would be equally cheap for Carly's family in this case.