You want to choose one long distance telephone company from

You want to choose one long distance telephone company from the following options: Company A charges $0.36 dollars per minute (no fixed monthly charge). Company B charges $13.7 per month plus $0.18 per minute. Company C charges a fixed rate of $50 per month. Let A(x), B(x), and C(x) denote the monthly charges of Company A, B, and C respectively for spending x minutes on long distance calls. (a) Find a formula for the monthly cost of using Company A, A(x): A(x) = (b) Find a formula for the monthly cost of using Company B, B(x): B(x) = (c) Find a formula for the monthly cost of using Company C, C(x): C(x) = (d) If you spend 125 minutes talking long distance in a month, which of the three companies will be cheapest? Enter the letter (A, B, or C) here:

Solution

Solution:

If x is the number of minutes, then

Company A will charge you 0.36x per month

Company B will charge you 13.7 + 0.18x per month

Company C will charge you 50 per month

Company B is cheapest with respect to Company A when the following inequality is true

13.7 + 0.18x < 0.36x

13.7 < 0.36x-0.18x

x < 13.7/0.18

x < 76.11 minutes.

Company B is cheapest with respect to Company C when the following inequality is true:

13.7 + 0.18x < 50, or

x < 201.667 minutes.

Thus, Company B is cheapest if you talk less than 86 minutes a month.