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 $10.00 with a charge of $0.15 per minute for all long-distance calls. Complete parts a and b.
a) Let's denote L as the number of minutes of long-distance calls made in a month. The total cost for Plan A can be calculated using the formula:
Total cost for Plan A = Monthly fee + (Charge per minute x Number of minutes)
So, for Plan A, the total cost would be:
Total cost for Plan A = $45.00 + ($0.05 x L)
Simplifying, we get:
Total cost for Plan A = $45.00 + $0.05L
The total cost for Plan B can be calculated using the same formula:
Total cost for Plan B = Monthly fee + (Charge per minute x Number of minutes)
So, for Plan B, the total cost would be:
Total cost for Plan B = $10.00 + ($0.15 x L)
Simplifying, we get:
Total cost for Plan B = $10.00 + $0.15L
b) To decide which plan is more cost-effective, we need to compare the two total cost formulas we found in part a. By setting the two formulas equal to each other, we can find the point where the total cost for each plan is equal and determine the range of minutes for which each plan is best.
$45.00 + $0.05L = $10.00 + $0.15L
Subtracting $0.05L and $10.00 from both sides, we get:
$45.00 - $10.00 = $0.15L - $0.05L
$35.00 = $0.10L
Dividing both sides by $0.10, we find:
L = $35.00 / $0.10
L = 350
Therefore, when the number of minutes of long-distance calls made in a month is 350 or more, Plan A is more cost-effective. For any number of minutes less than 350, Plan B is the better option.