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Math Help - splitting profits by percentages

  1. #1
    Newbie
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    Jul 2009
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    Question splitting profits by percentages

    Hi, any help would be great.

    I need to work out a way of splitting different percentages of a profit between people.

    Example #1:
    Ten people split the profit (1000) between them. But not equally.
    4 people (A-D) need to get 30% more than the other 6 people (E-J).
    I have worked this out manually as:
    A 11.6% 116.00
    B 11.6% 116.00
    C 11.6% 116.00
    D 11.6% 116.00
    E 8.93% 89.30
    F 8.93% 89.30
    G 8.93% 89.30
    H 8.93% 89.30
    I 8.93% 89.30
    J 8.93% 89.30
    (1000.00)

    Is there an equation to work this out?

    I need to work out many more percentage splits and by different amounts of people.

    Example #2:
    Ten people split the profit between them. But not equally.
    3 people (A-C) need to get 40% more than the other 7 people (D-J).

    ...I could work it out manually... But I need it as an equation so i can change the number of people who receive more and the percentage relative to the others that they receive. I will also need to work this out for 8 people and 6 people etc... and get it into a Exel spreadsheet!

    Please help - I can't get my head round it!!!
    Thanks,
    Scott
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  2. #2
    Senior Member
    Joined
    Jul 2009
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    397
    Hi AtAdj

    Let :
    money received by A-D each = x
    money received by the rest = y

    x = 1.3 y----------> equation 1, because x is 30 % higher than y

    4x + 6y = 1000---> equation 2

    you can replace 4 or 6 with the number of people you desired
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  3. #3
    MHF Contributor
    Joined
    Dec 2007
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    Ottawa, Canada
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    General case (with example using your first one):

    a = amount (1000)
    t = total persons (10)
    n = number of persons getting MORE (4) ; n < t
    r = percent MORE (30)
    x = lower amount (?)

    x = a / (t + nr/100)

    x = 1000 / (10 + 4(30)/100) = 89.2857... (you got 89.30)
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