You are choosing between two telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all calls. Plan B has a monthly fee of $3 with a charge of $0.12 per minute for all calls. How many calling minutes in a month make plan A the better deal?
15 + .08 x = 3 + .12 x
s
12 = .04 x
x = 1200/4 = 300
To determine how many calling minutes in a month make plan A the better deal, we need to compare the total cost of both plans based on the number of minutes used.
Let's assume x represents the number of calling minutes used in a month.
For plan A, the total cost can be calculated as:
Cost_A = $15 (monthly fee) + $0.08 (cost per minute) * x (number of calling minutes)
For plan B, the total cost can be calculated as:
Cost_B = $3 (monthly fee) + $0.12 (cost per minute) * x (number of calling minutes)
To find out when plan A becomes the better deal, we need to set up an inequality where the total cost of plan A is less than the total cost of plan B.
Cost_A < Cost_B
$15 + $0.08x < $3 + $0.12x
First, we move all the terms with x to one side:
$0.08x - $0.12x < $3 - $15
Simplifying both sides, we get:
-$0.04x < -$12
Next, we multiply both sides by (-1) to switch the inequality sign:
$0.04x > $12
Dividing both sides by $0.04, we get:
x > $12 / $0.04
Simplifying further, we have:
x > 300
Therefore, for any number of calling minutes greater than 300, plan A will be the better deal.
In summary, plan A becomes the better deal when you expect to use more than 300 calling minutes in a month.