A cell phone company charges

Question

A cell phone company Ringer charges $7.46 per month plus $0.13 a call another cell phone company Busy charges $6.17 plus $0.17 per call

Fill in the table to estimate when Ringer charges less than Busy

Answer 1

To solve this problem, you need to start with the monthly charge, and then add to it the cost of each call made. To calculate the total cost, you start with the monthly cost. Then multiply the number of calls times the cost/call. Then add that number to the monthly cost.

Since I do not know what your table looks like, here is an example of how the cost changes with more calls. You will need to fill in your table completely, and you will find that the Busy becomes cheaper than Ringer somewhere between 30 and 50 calls. Look at the total cost in each cell in YOUR table carefully, and find where the switchover occurs.

Company	Monthly Charge	Cost for each call	Total cost for 1 call	Total cost for 2 calls		Total cost 10 calls	Total cost 30 calls	Total cost 50 calls
Ringer	7.46	0.13	7.46 + .13 = 7.59	7.46 + .26 = 7.72		7.46 + 1.30 = 8.76	7.46 + 3.90 = 11.36	7.46 + 6.50 = 13.96
Busy	6.17	0.17	6.17 + 0.17 = 6.34	6.17 + 0.34 = 6.51		6.17 + 1.70 = 7.87	6.17 + 5.10 = 11.27	6.17 + 8.50 = 14.67

Answer 2

Hello, Tt,

We can model the monthly cost of each phone campany as a function of the number of calls, x, in a month.

Let R = Total monthly cost for Ringer, and B = Total monthly cost for Busy

The total cost will be the montly fee plus the number of calls (in a month) times the per call charge for each company.

R = ($0.13/call)*x + $7.46

B = ($0.17/call)*x + $6.17

Written this way, we can see that company B has a steeper slope by lower y-intercept, the cost for when no calls are made (x=0). Company R has a higher monly cost, by the slope of 0.13 means that there will be some point when company B's cost will be greater, since the slope for B is greater.

We can either plot these lines on Desmos and look for the point of intersection (I found (32.5, 11.5)) or set each equation equal to each other and solve for x (calculate the number of calls would it take for the cost of B equal R).

0.13x + 7.46 = 0.17x + 6.17

x = 32.25 calls/month

At 32.25 [32] calls/month and up, the cost for Busy exceeds the cost for Ring.

Ringer charges less than Busy up to 33 calls/month.

Bob