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A real life problem

  1. Jun 23, 2010 #1
    I'm a collage student, I rented an apartment flat with my 2 friends. We bought all house things by each of us paying 1/3 of their price.

    An now we are to break apart, I decided to make a drawing (like lottery) to decide who take which house hold.

    Assume that,
    A, B, C: Names of three people
    T: Total cost of all household goods
    N: Total number of all all household goods
    ai: Cost of element of set of the household goods that A takes as a result of the drawing
    bi: Cost of element of set of the household goods that B takes as a result of the drawing
    ci: Cost of element of set of the household goods that C takes as a result of the drawing
    m: Number of household goods that A takes as a result of the drawing
    n: Number of household goods that B takes as a result of the drawing
    k: Number of household goods that C takes as a result of the drawing

    Can you give me the function f defined as,
    f(person1, person2): Amount of money that person1 pays to person2
    in terms of the parameters listed above.
     
  2. jcsd
  3. Jun 23, 2010 #2

    CompuChip

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    Science Advisor
    Homework Helper

    It only depends on what each person ends up taking, since everyone has already paid 1/3, doesn't it?

    So suppose A takes 1/2 of all the goods, B takes 3/8 and C takes 1/8.
    Then A will have to deposit (1/2 - 1/3)T in the common bank account and B should pay (3/8 - 1/3)T, while C gets to withdraw (1/3 - 1/8)T.

    If you want, you can skip the bank account and settle it directly by making A pay (1/2-1/3)T to C directly, and let B pay (3/8-1/3)T to C.
     
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