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

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $44.95 plus 8 cents per minute. 

Answer 1

The question asks:    "When will cost of second plan < cost of first plan?"

 

Let x = number of minutes used in a month.

 

       cost of second plan        <       cost of first plan

           $44.95 + $0.08x       <       $0.23x

           4495 + 8x < 23x                            [divide by $; multiply by 100]

            4495 < 15x                           [subtract 8x from both sides]

           15x > 4495                         [reverse sides]

             x > 299 2/3 minutes

 

Let's check at 300 minutes:

   Is     cost of first plan > cost of second plan    ?

        $0.23(300)  >  $44.95 + $0.08(300)    ?

          $69.00  >  $68.95    ? yes