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Math Help - Simple division

  1. #1
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    Simple division

    A doctor currently makes $175,000 in profit: $425,000 in revenue and $250,000 in cost. The physician's time spent is on 75% patient care, 15% billing, and 10% administrative services. If a doctor outsources his billing, he can spent the 15% of the time he spent billing seeing patients. How much extra revenue does he earn if billing is outsourced?

    The correct answer is:

    ($425,000 x 15%)/(75%)=$85,000.

    I simply don't understand why you would divide the 75%. Can anyone enlighten me? Thanks.
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  2. #2
    MHF Contributor
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    Re: Simple division

    Hey phi1234.

    The total revenue for billing purposes is currently $425,000 x 15% = $63,750. We want to get a unit of revenue per unit time and this is where the 75% comes in.

    Dividing by 75% is the same as finding the "revenue per unit time" figure since the 75% corresponds to the actual amount of time that the physician earns money: remember that he doesn't earn money on administrative and billing work but only on face-to-face time.

    So to get a standard measure of "revenue per unit time" we need to divide by 75% since we have now taken the other two roles away which are freed up by the outsourcing.

    Recall that with the other roles patient time is 75% and without these patient time is 100%. The ratio of these is 100%/75% = 1/75%.

    This 1/75% is a conversion factor of going from one distribution of activities to another.
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