You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $45.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $5.00 with a charge of $0.15 per minute for all long-distance calls. Complete parts a and b.
a) Write an equation for each plan to represent the total cost, C, (in dollars) based on the number of minutes, m, of long-distance calls made in a month.
For Plan A, the equation is: C = 45 + 0.05m
For Plan B, the equation is: C = 5 + 0.15m
b) Determine the number of minutes of long-distance calls that make the two plans equal in cost.
To find the number of minutes, m, where the two plans have the same cost, we set the equations equal to each other and solve for m:
45 + 0.05m = 5 + 0.15m
Subtracting 0.05m from both sides, we get:
45 = 5 + 0.10m
Subtracting 5 from both sides, we get:
40 = 0.10m
Dividing both sides by 0.10, we get:
400 = m
Therefore, the two plans will have the same cost when 400 minutes of long-distance calls are made.