Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $20 one-time activation fee and charges 13 cents a minute. The second plan has no activation fee and charges 17 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $20 one-time activation fee and charges 13 cents a minute. The second plan has no activation fee and charges 17 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

Answer 1

x = number of minutes

20 + .13x = .17x

Solve for x.

I hope this helps.

Answer 2

To find out after how many minutes of long distance calls the costs of the two plans will be equal, let's set up an equation using algebra.

Let's say the number of minutes of long distance calls is represented by 'm'.

For the first plan, the cost is given by the equation:
Cost of first plan = Activation fee + (Rate per minute * Number of minutes)
Cost of first plan = $20 + (0.13 * m)

For the second plan, the cost is given by the equation:
Cost of second plan = Rate per minute * Number of minutes
Cost of second plan = 0.17 * m

Now, to find the point where the costs of the two plans are equal, we can set up the equation:
$20 + (0.13 * m) = 0.17 * m

To solve this equation, we can begin by isolating the variable on one side:
$20 = (0.17 * m) - (0.13 * m)

Combining like terms:
$20 = 0.04 * m

Let's solve for 'm' by dividing both sides of the equation by 0.04:
$20 / 0.04 = m

m = 500

Therefore, after 500 minutes of long distance calls, the costs of the two plans, with the given activation fee and rates, will be equal.