You are choosing between two different cell phone plans. The first plan charges a rate of 25 cents per minute. The second plan charges a monthly fee of $29.95 in addition to 10 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

You would have to use over 200 minutes in a month in order for the second plan to be preferable.

Step-by-step explanation:

Let x represent the number of minutes that you use in a month.

The first plan charges a rate of 25 cents per minute. It means that the cost of using x minutes in a month with this plan is 0.25x.

The second plan charges a monthly fee of $29.95 in addition to 10 cents per minute. It means that the cost of using x minutes in a month with this plan is

29.95 + 0.1x

For the second plan to be preferable, its cost would be lesser than the first plan. Therefore,

29.95 + 0.1x < 0.25x

29.95 < 0.25x - 0.1x

29.95 < 0.15x

0.15x > 29.95

x > 29.95/0.15

x > 200

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.