You are choosing between two long-distance telephone plans. Plan Ahas a monthly fee of $35.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $15.00 with a charge of $0.10 per minute for all long-distance calls. Complete parts a and b.
a) Let x be the number of minutes of long-distance calls made in a month.
For Plan A, the total cost per month is given by:
Cost of monthly fee + Cost of long-distance calls = $35.00 + ($0.05 per minute)x = $35.00 + 0.05x.
For Plan B, the total cost per month is given by:
Cost of monthly fee + Cost of long-distance calls = $15.00 + ($0.10 per minute)x = $15.00 + 0.10x.
So, the expression for the total cost per month for Plan A is $35.00 + 0.05x, and for Plan B is $15.00 + 0.10x.
b) To compare the two plans, we need to set up an equation and solve for the number of minutes, x, when the total costs are equal.
The equation is:
35 + 0.05x = 15 + 0.10x.
Subtracting 0.05x from both sides:
35 = 15 + 0.05x,
20 = 0.05x.
Dividing by 0.05:
x = 400.
Therefore, if the number of minutes of long-distance calls made in a month is 400 minutes or less, Plan A will be cheaper. If the number of minutes of long-distance calls made in a month is more than 400 minutes, Plan B will be cheaper.