Customers of a phone company can choose between two service plans for long distance calls. The first plan has a one time activation fee of $26 and charges 8 cents a minute. The second plan has no activation fee and charges 13 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

2600 + 8x = 13 x

To find the number of minutes at which the costs of the two plans are equal, we need to set up an equation and solve for the unknown minutes.

Let's calculate the cost for each plan:
- The first plan has a one-time activation fee of $26 and charges 8 cents per minute. So the cost for the first plan will be 26 + 0.08x, where x is the number of minutes.
- The second plan has no activation fee but charges 13 cents per minute. So the cost for the second plan will be 0 + 0.13x.

Now, we can set up an equation to find the equal costs:
26 + 0.08x = 0 + 0.13x

To solve this equation, we can begin by subtracting 0.08x from both sides:
26 = 0.05x

Next, divide both sides of the equation by 0.05:
26 / 0.05 = x

Simplifying this expression, we get:
520 = x

Therefore, after 520 minutes of long-distance calls, the costs of the two plans will be equal.