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I am trying to calculate a weighted average where the final answer is known, but the multiplier is not.

So I want to know is, if I have a formula such as $30x + 40.3y + 27.8z = 55$, where $x$, $y$ & $z$ will always add to 100%, what are the possible values of $x$, $y$, & $z$. Is there a simple way to do this in excel, or something similar? I would like something that would tell me all the possible combinations of $x$, $y$, and $z$.


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There are an infinite number of combinations of x, y, and z. Are there any other restrictions on your variables? – Simon Hayward Dec 7 '12 at 15:28

Unless you have a further restriction on your variables then they will be able to take an infinite range of values in $\mathbb{R}$.

We have two restrictions, the first one, and $x + y +z =100$, but two equations in three variables will always have one free variable.

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