TITLE: Weighted division?
QUESTION [5 upvotes]: 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?

REPLY [8 votes]: 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 $k=1,2,\dots,10$)
$$10000\cdot\frac{x_k}t\text{ dollars}\;.$$