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Let's say I have 10,000 dollars I want divided among 10 people. With simple division each person gets $1,000. Easy enough.

Now suppose each person has a score on a test from 0 to 200. Now I want to divide the money among all the people but weighted by their score on the test, such that people who scored higher will get more money. How would I do that?

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    $W=\frac{Individual~ test~ score}{sum~ of~ all~ test~ scores}$2012-12-07

1 Answers 1

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Suppose that the test scores are $x_1,x_2,\dots,x_{10}$. Let $t$ be the sum of the test scores; then the first person’s share of the total is $\frac{x_1}t$, the second’s is $\frac{x_2}t$, and so on. These ten fractions add up to $1$, so just give person $k$ (for $k=1,2,\dots,10$)

$10000\cdot\frac{x_k}t\text{ dollars}\;.$

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    ... satisfactory results.2012-12-11