A cell phone service provider offers two plans. Plan A includes a fee of $25 per month and charges $0.25 for every call. Plan B includes a fee of $40 per month and offers unlimited calls. For what number of phone calls is the cost of plan B less than the cost of plan A?

Question

16-10-2017
Mathematics

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A cell phone service provider offers two plans. Plan A includes a fee of $25 per month and charges $0.25 for every call. Plan B includes a fee of $40 per month and offers unlimited calls. For what number of phone calls is the cost of plan B less than the cost of plan A?

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randybaker randybaker · Answer 1 · 2017-10-28T21:06:50+02:00

This problem is a classic algebra problem. Let's use our variables to create some equations.

The total cost of Plan A is mx+b, where b is the inital monthly cost of the plan and m is the rate charged per call. x is the number of phone calls received in the month. With this in mind, we know that the total cost of one month of Plan A is f(x)=.25x+25

The total cost of Plan B is simpler. It's just $40.

Now we need to figure out the number x that will make Plan B<Plan A.

40<.25x+25

x=60

Therefore, Plan B costs less than Plan A after 60 phone calls have been made.