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Math Help - Percent Allocation

  1. #1
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    Percent Allocation

    Hi,
    I am not sure my thought process is correct in this computation. I need to allocate a portion of the tax $500 between these amounts $1500 and $2000 relative to their percentage of the total $4000.

    1) $1500+$2000+500(tax) = $4000
    2) 1500/4000 = .375
    2000/4000 = .5
    500/4000 = .125
    3) 500*.375 = 187.50
    500*.5 = 250.00
    500*.125 = 62.50
    4) 1500+187.50 = 1687.50
    2000+250.00 = 2250.00
    3937.50
    What about the remaining 62.50? How does that get allocated between $1500 and $2000 or does that get allocated at all? That's the part that is confusing me. Can someone please help explain what I'm doing wrong? Thanks!
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  2. #2
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    tax $500 between these amounts $1500 and $2000 relative to their percentage of the total $4000.

    What? There should not be a remaining 62.50. Something went wrong. Please remember that results should make sense. When your solution fails to make sense, rework your arithmetic, don't question the mathematics.

    (2000 / 4000) * 500 = (1/2) * 500 = 250

    (500 / 4000 ) * 500 = (1/8) * 500 = 62.50

    Since we like to avoid rounding errors, 500 - 250 - 62.50 = 187.50

    Now check

    (1500 / 4000 ) * 500 = (3/8) * 500 = 187.50

    Now you are done.

    Of course, in this case, figuring out what the problem is and what it wants turns out to be the hard part.
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  3. #3
    MHF Contributor

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    Quote Originally Posted by CherylSedor View Post
    Hi,
    I am not sure my thought process is correct in this computation. I need to allocate a portion of the tax $500 between these amounts $1500 and $2000 relative to their percentage of the total $4000.

    1) $1500+$2000+500(tax) = $4000
    2) 1500/4000 = .375
    2000/4000 = .5
    500/4000 = .125
    You should not be including the tax in the total: $1500+ $2000= 3500.
    1500/3500= 0.429, 2000/3500= 0.571 (and, of course, .429+ .571= 1.000)
    .571*500= $285.50 500*.429= $214.50 and, again, 285.50+ 214.50= 500.
    $285.50 of the tax is allocated to the $2000 and $214.50 to the $1500.

    3) 500*.375 = 187.50
    500*.5 = 250.00
    500*.125 = 62.50
    You are allocating $62.50 of the tax to the tax. You don't have to pay tax on tax!

    4) 1500+187.50 = 1687.50
    2000+250.00 = 2250.00
    3937.50
    What about the remaining 62.50? How does that get allocated between $1500 and $2000 or does that get allocated at all? That's the part that is confusing me. Can someone please help explain what I'm doing wrong? Thanks!
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