You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $25.00 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 $0.15 per minute for all long-distance calls. Complete parts a and b.
To compare the two long-distance telephone plans, let x be the number of minutes of long-distance calls made per month.
a) The cost for Plan A can be calculated using the formula:
Cost(A) = Monthly fee + (Charge per minute * Number of minutes)
Cost(A) = $25 + ($0.05 * x)
Cost(A) = $25 + $0.05x
The cost for Plan B can be calculated using the formula:
Cost(B) = Monthly fee + (Charge per minute * Number of minutes)
Cost(B) = $15 + ($0.15 * x)
Cost(B) = $15 + $0.15x
b) To determine at what minute value, both plans have an equal cost, we can set the cost formulas equal to each other and solve for x:
$25 + $0.05x = $15 + $0.15x
Subtracting $0.05x and $15 from both sides:
$25 - $15 = $0.15x - $0.05x
$10 = $0.10x
Dividing both sides by $0.10:
x = $10 ÷ $0.10
x = 100
Therefore, when the number of minutes of long-distance calls is 100, both plans will have an equal cost.