You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $39.95 plus 12 cents per minute

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $39.95 plus 12 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

Answer 1

Hi Joe,

How many minutes would you have to use in a month in order for the second plan to be preferable?

Plan 1 cost : .22 per min

Plan 2 cost: 39.95 + .12 per min

Let x = number of minutes

Let y = Monthly Fee

Plan 1 cost: y = .22x

Plan 2 cost: y = .12x + 39.95

Think about how these two equations are graphed. Plan 1's line passes through (0,0), indicating its initial charge at 0 minutes is $0. But Plan 2's line has a y intercept of 39.95, indicating that at 0 minutes its initial charge is $39.95. But Plan 1 has a larger slope than Plan 2. Because of this we know that Plan 1 will be preferable until a point in time when Plan 2 will become preferable.

To find this point, we would set the two equations equal to each other to see at what number of minutes their monthly fee is the same.

Plan 1 = Plan 2

.22x = .12x + 39.95

.10x = 39.95

x = 399.5 minutes

This means that at x = 399.5 minutes the monthly charge would be the same. At any number of minutes below this, plan 1 would be preferable, at any number of minutes above this, plan 2 would be preferable.

You would need to use above 400 minutes for Plan 2 to be preferable.

Answer 2

Let x = minutes

1st plan = 0.22x

2nd plan = 39.99 +0.12x

How many minutes would make the cost the same?

1st plan = 2nd plan

If the 2nd plan is preferable, it needs to cost "less than" the 1st plan.

1st plan > 2nd plan

Solve the inequality and you'll see how many minutes more.

Answer 3

Let x be the number of minutes. The two plans would have to cost the same before the second plan is preferable.

Plan 1: y = .22x

Plan 2: y = .12x + 39.95

.22x = .12x+ 39.95

.1x = 39.95

x = 39.95/.1 = 399.5 minutes

After that, you'd be saving 10 cents a minute.

So it depends if you talk more than 6.66 hours a month or ≈ 0.6 minutes a day.