Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $29

monthly fee and charges an additional 0.09
for each minute of calls. The second plan has no monthly fee but charges
0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

For this problem, you have to come up with two equations, one for each plan, and set them equal to each other to solve for how many minutes of calls when the costs of the two plans are equal. Let's call the number of minutes "x." Remember the equation for slope-intersect form is:

`y=mx+b`
And we're trying to put in values for m and b.

So the first plan has a $29 monthly fee and charges an additional $0.09 per minute. The $29 monthly fee will be our "b" in our slope-intersect equation because it won't be affected by our minutes "x." That means 0.09 is our "m" value because it will change with "x." So our equation for plan 1 is:

`y=0.09x+29`

The second plan has no monthly fee but charges 0.13 for each minute of calls. Because there is no monthly fee, there is no "b" this time. "m" will be 0.13. So our equation for plan 2 is"

`y=0.13x`

Now we set our two equations equal to each other. "y" in the equation stands for the total cost of the plan. If the total costs are equal, then they have to be the same number, so we can put one of the equations for "y" into the other equation and solve for "x," our number of minutes:

`0.13x = 0.09x+29 \\ 0.04x = 29 \\ x = 725 \: minutes`