Customers of a phone company can choose between two service plans for long-distance calls. The first plan has no monthly fee but charges $.11 for each minute of calls. The second plan has a $27.00 monthly fee and charges an additional $.07 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
when is .11n = .07n + 27 , where n is the number of calls
To find the number of minutes of calls for which the costs of the two plans are equal, we need to set up an equation.
Let's assume the number of minutes of calls is represented by 'x'.
For the first plan, the cost is calculated by multiplying the number of minutes by the rate of $0.11 per minute. So, the cost of the first plan would be 0.11x.
For the second plan, there is a fixed monthly fee of $27.00, and for each minute, an additional cost of $0.07 per minute. The total cost of the second plan can be calculated by adding the fixed fee and the cost per minute, multiplied by the number of minutes. So, the cost of the second plan would be 27 + 0.07x.
To find the number of minutes for which the costs of both plans are equal, we can set up the equation:
0.11x = 27 + 0.07x
Simplifying the equation:
0.11x - 0.07x = 27
0.04x = 27
Now, solve for 'x' by dividing both sides of the equation by 0.04:
x = 27 / 0.04
Using a calculator, we find:
x = 675
Therefore, the costs of the two plans will be equal when there are 675 minutes of calls.