Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges $ 0.14 for each minute of calls. The second plan has a $ 22 monthly fee and charges an additional $ 0.10 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Hey there!

We'll define x as the amount of minutes for a call.

The monthly fee is the initial value, while the cost per call is te constant. The cost per call is the coefficient of x because you're multiplying the cost/call times the number of calls.

Now, we'll look at the first company, that has no monthly fee. However, it has 14 cents/minute, so we have:

y = .14x

For the second one, we have a 22 dollar upfront fee, along with 10 cents per call. In this problem, the 10 cents is the cost per call, or the coefficient of x.

We have:

y = 22 + .10x

Now, to see when the minutes of calls will equal to when the costs are equal, we set both equations equal to each other because we want to see the value of x that works on the left and right side of the equation:

22 + .10x = .14x

Subtract .10x from both sides:

22 = .04x

Divide both sides by .04:

x = 550

If we plug it back in, we get:

22 + .10(550) = .14(550)

77 = 77

Therefore, you would need 550 calls.

Hope this helps!