Would someone please solve this problem for me and explain how you got the answer? Thanks?

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $30 one-time activation fee and charges 10 cents a minute. The second plan has no activation fee and charges 14 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

Let m = #minutes used

Plan A = 30 + .10m
Plan B = .14m

Where they are equal:

30 + .10m = .14m

Solve for m:

30 = 0.04m

m = 30/.04 = 750 minutes

This is actually to do with solving equations.

The cost of Plan 1 can be written as 3000 + 10x while the cost of Plan 2 can be written as 14x where x is the number of minutes.

We are interested when the cost of the two plans is equal. This just means we need to set the equations equal to each other and try to solve for x.

Cost Plan 1 = Cost Plan 2

=> 3000 + 10x = 14x

Now rearrange:

=> 3000 = 14x - 10x
=> 3000 = 4x

=> x = 750

Therefore when x=750 minutes, the cost of the two plans will be equal.

Let y be the total cost, fixed cost plus the product of time in minutes by the charge per minute.
Let x = the number of minutes
Case 1) y = 10x + 300 cents = cost incurred in x minutes

Case 2) y = 14x cents = cost incurred in x minutes

The breakeven point will occur when the two cases are equal.

Then 14x = 10x + 300
4x = 300
x = 75 minutes

Sorry guys I just see from the rest of your answers that you do not multiply 30 by 100 and get 300.

Well, lets try this!
$.14/30 = 214.285714 minutes
I'm not exactly sure what your asking.
214.285714 + $.10/min = 235.714281
This is a tricky problem....

Don't trust this answer, but I hope it gives you a general idea of what to do.

Hope this helps,
Erik T