High School Optimizing Fair Distribution of Pooled Funds among Debtors

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The discussion focuses on the mathematical challenge of fairly distributing pooled funds among debtors who are owed different amounts. The user seeks an efficient method to calculate how much each person should receive to minimize total dollar losses, given that the pooled funds are insufficient to cover all debts. A proposed solution involves calculating the total amount owed, determining the shortfall, and then evenly distributing that shortfall across all debtors. By subtracting the same shortfall from each individual's owed amount, the distribution can be balanced. The conversation highlights the need for both mathematical understanding and practical application, potentially using Excel for visualization.
mrcleanhands
Firstly, I'm not even sure how to frame this mathematically, but I'd be curious to know what kind of problem it is and what kind of subjects within maths it requires to be able to solve it.

Here's my problem--
I've set it up in excel to help you visualise it.
sss.png

There is a different amount of money owed to different people (Amounts Owed). There is a fund which'll be used to pay out those people (Pooled funds). The pooled funds do not equal the total amount owed. If I divide the amount of pooled funds by 4 and hand it out to each person evenly, the dollar loss amounts will be uneven (since each person is owed a different amount). What I'm trying to do is solve for values highlighted green (how much money is given to each person) such that the total dollar losses for each person will equal (that red column).

Is there some way to do this on paper very efficiently, or is it only a problem for the computer?
 

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1) Calculate the total owed.
2) Subtract the total pooled funds from that.
3) Divide the result by the number of people and label it $x. (That tells you how much short the pooled funds are per person.)
4) Give each person the amount owed minus $x.

Then each person will get what he is owed minus the same amount, $x.
 
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Just divide the total amount that you're short by 4, and subtract that from the amount owned for every person.
 

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