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)For how many minutes of long-distance calls will the costs for the two plans be the same?
Let's define the number of minutes of long-distance calls as x.
For Plan A, the cost is $45.00 + $0.05x.
For Plan B, the cost is $5.00 + $0.15x.
To find the number of minutes for which the costs for the two plans are the same, we need to set the costs equal to each other and solve for x:
$45.00 + $0.05x = $5.00 + $0.15x.
Subtracting $0.05x and $5.00 from both sides, we get:
$45.00 - $5.00 = $0.15x - $0.05x.
$40.00 = $0.10x.
Dividing both sides by $0.10, we get:
x = $40.00 / $0.10.
x = 400 minutes.
So, for 400 minutes of long-distance calls, the costs for the two plans will be the same.
B) Let's calculate the cost of each plan for 200 minutes of long-distance calls:
Plan A: $45.00 + $0.05(200) = $45.00 + $10.00 = $55.00.
Plan B: $5.00 + $0.15(200) = $5.00 + $30.00 = $35.00.
Therefore, for 200 minutes of long-distance calls, Plan A costs $55.00 and Plan B costs $35.00.