You are choosing between two different prepaid cell phone plans. ONE charges a rate of 32 cents/minute. The second charges a monthly fee of $19.95 plus 17 cent

Question

You are choosing between two different prepaid cell phone plans. ONE charges a rate of 32 cents/minute. The second charges a monthly fee of $19.95 plus 17 cents/minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

Answer 1

We want to know at what point $19.95 + $.17(#mins)

will be less than $.32(#mins)

 

Letting m=# minutes used, your equation is:

 

19.95 + .17m < .32m

Subtract .17m from both sides

19.95 < .32m - .17m

19.95 < .15m

Divide both sides by .15 to isolate 1 m

19.95/.15 < m

 

133 < m

 

If we use more than 133 minutes then the 2nd plan will be cheaper.

 

Verify:  If we use 133 minutes in plan 1:

            Cost = .32(133) = $42.56

     

            Using 133 minutes in plan 2:

            Cost = .17(133) + 19.95 = $42.56

 

            At 133 minutes the plans cost the same amount.

      

           Pick a number greater than 133 minutes and verify that

           plan 2 is cheaper.  Let's use 134 minutes.

 

           Plan 1: .32(134) = $42.88

           Plan 2: .17(134) + 19.95 = $42.73

 

           As expected, once past 133 minutes plan 2 is cheaper.