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I am trying to figure out how to create a formula to solve this problem I have.

OK, the problem

I need to work how much money to give people bassed on a percentage of a total value, but the problem is that the percentage varies from person to person.

Ie,

Total amount = $1,000,000

Total People = 100

90 people get 100% of $1,000,000 / 100 people

5 people get 80% of $1,000,000 / 100 people

3 people get 60% of $1,000,000 / 100 people

2 people get 40% of $1,000,000 / 100 people

Now the issue I am having is that not even one cent can be left over. Do I just work out based on what each person would get $1,000,000 / 100 people and then just divding the remainder?

ie,

$1,000,000 / 100 = 10,000

10,000 * 100% = $10,000

10,000 * 80% = $8,000

10,000 * 60% = $6,000

10,000 * 40% = $4,000

And the total of that

90 x 10,000 = $900,000

5 x 8,000 = $40,000

3 x 6,000 = $18,000

2 x 4,000 = $8,000

Total of $966,000, remaining 34,000 dollars to be divided by 100 and added to each persons figure.

Or is there a better way to go about this?

EDIT: Another way I thought of doing this would be to have anyone who gets less than a 100% share, have it so they get the desired percentage of the full share people.

ie, Say a full share worked out to be, 10,340 Dollars, have someone who gets an 80% share get 8,272 dollars etc and so on.

I just need to know how to get this worked out in a simple equation.

Thank for the help. And could someone edit the tags, I have no idea what to tag this with.

1 Answers 1

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The problem is that, as you observe, the numbers don't add up.

This can be restated in a simpler form: "I have to distribute all of $100 to two people. One gets 40%; the other gets 45%. How much should I give to each?" Well, if I give one $40 and the other $45, I've split it 40%/45%, but haven't given away the last $15. If I give either one of them part of the $15, they won't be getting $40 and $45, so I won't be following the rules.

So the answer to your problem is "There's no distribution of money that satisfies the rules given." Because there's only one way for each person to get the amounts specified (which you've written out!) and that allocation does not use up all the money.

It really is as if you were told "Give all this money to Joe. And make sure he gets exactly 83% of it." It's not your fault that you cannot carry out this instruction; the instruction itself is internally contradictory.

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    I understand what you mean, but, the best solution would be for the people not receiving 100%, would be to have them receive exactly 80%,60% and 40% of the value that the 100% people are getting. How would I do that. – 2017-01-12
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    There's no "best solution" to a problem that has no answer. You need to ask a different question (or clarify this one) until it actually has an answer; at that point, someone may be willing to write a formula for you. – 2017-01-12