Customers of a phone company can choose between two service plans for long distance calls. The first plan has a one-time activation fee and charges cents a minute. The second plan has no activation fee and charges cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?
To determine the number of minutes when the costs of the two plans are equal, we need to set up an equation based on the given information.
Let's assume that after x minutes of long-distance calls, the costs of the two plans will be equal.
For the first plan, the cost will be the sum of the one-time activation fee and the product of the per minute cost and the number of minutes:
Cost of plan 1 = Activation fee + (x * cents per minute)
For the second plan, since there is no activation fee, the cost will be only the product of the per minute cost and the number of minutes:
Cost of plan 2 = (x * cents per minute)
We can set up an equation to represent the situation:
Activation fee + (x * cents per minute) = (x * cents per minute)
Now we can solve this equation to find the value of x.
First, subtract (x * cents per minute) from both sides of the equation:
Activation fee = 0
Since the activation fee is zero for the second plan, it means that the activation fee for the first plan is also zero (as mentioned in the problem statement).
So, we can simplify the equation to:
0 + (x * cents per minute) = (x * cents per minute)
Now, subtract (x * cents per minute) from both sides again:
0 = 0
The equation simplifies to 0 = 0, which is always true. This means that there is no value of x that will make the costs of the two plans equal.
Therefore, it is not possible for the costs of the two plans to be equal regardless of the number of minutes of long-distance calls made.