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Break even on cell phone plans

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data
    A customer is choosing between two cellular phone plans.
    One plan has a monthly fee of $50 for an allowance of
    500 minutes per month. If the customer uses more than
    500 minutes, the charge is $0.35 per additional minute used.
    The other plan has a monthly fee of $75 for an allowance of
    1000 minutes per month. If the customer uses more than
    1000 minutes, the charge is $0.40 per additional minute. After
    how many minutes used are the monthly costs of the plans
    equal?



    2. Relevant equations
    This is how I set it up....
    Plan 1: (<=500 min) x= $50; (>500 min) x= $50 + $0.35m
    Plan 2: (<=1000 min) x= $75; (>1000 min) x= $75 + 0.40m




    3. The attempt at a solution
    The answer is 4000 minutes, but I don't know how to proceed. Any help is appreciated.
     
  2. jcsd
  3. Feb 4, 2013 #2

    Mark44

    Staff: Mentor

    A better choice would be C, for cost, and then either x or m for the number of minutes.
    For starters, try graphing both cost functions on the same axis system. For plan 1, the graph is a horizontal line 50 units up for m in the interval [0, 500]. Then the graph heads off at a slope of .35.

    See if you can figure out what the graph for plan 2 looks like, as well.
     
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