Question

Jane has a pre-paid cell phone with A Fee and Fee. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 220 minutes and the cost was $124.00. In July she used 710 minutes and the cost was $344.50.Express the monthly cost C as a function of x , the number of minutes of calling time she used. If Jane used 764 minutes of calling time in August, how much was her bill?

Answer 1

To find the cost of Jane's pre-paid cell phone bill based on the minutes used, one must first establish the monthly fee and per-minute charge by solving a system of equations. Then, the monthly cost can be expressed as a function of the number of minutes used. Once that function is known, calculating the bill for any number of minutes is straightforward.

Step-by-step explanation:

Jane has a pre-paid cell phone with a monthly fee and a charge for each minute of calling time. Given the costs for two different months, we can set up a system of equations to find the monthly fee and the per-minute charge. Let's denote the monthly fee as M and the per-minute charge as C. From the given information:

• In June, she used 220 minutes and her cost was $124:
  M + 220C = $124
• In July, she used 710 minutes and her cost was $344.50:
  M + 710C = $344.50

By solving this system of equations, we get M (monthly fee) and C (per-minute charge). Once we have C, we can express the monthly cost as C(x) = M + xC, where x is the number of minutes used.

To calculate Jane's bill for August when she used 764 minutes, just substitute x with 764 in the expression C(x).