<s>[INST] Calculating Inverse Proportion of 5 or more variables I am trying to create a formula to calculate a wine blend based on the relative boldness (on a scale of 0-100) of each of the five blending components.  At this stage, I am assuming that each component is equally liked by the taster and in order to give equal weight to the components in the blend, relative boldness is inversely proportional to the quantity of each component added.
If:
$$\ a∝b∝c∝d∝e$$
I first calculated the percentage of each component assuming they were proportional:
$$\frac{100a}{a+b+c+d+e}  +\frac{100b}{a+b+c+d+e}+\frac{100c}{a+b+c+d+e}+\frac{100d}{a+b+c+d+e}+\frac{100e}{a+b+c+d+e}$$
I then calculated the inverse of each component:
$$\frac{a+b+c+d+e}{100a}+...+\frac{a+b+c+d+e}{100e}$$
and divided each by the sum of the inverse of the percentage of each component:
$$\frac{a+b+c+d+e}{100a(\frac{a+b+c+d+e}{100a}...\frac{a+b+c+d+e}{100e})}+...+\frac{a+b+c+d+e}{100e(\frac{a+b+c+d+e}{100a}...\frac{a+b+c+d+e}{100e})}$$
I then simplified the formula:
$$\frac{1}{a(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e})}+...+\frac{1}{b(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e})}$$
I tested the above method with three variables against the following formula for inverse proportions for three variables and got the same answer so I am assuming that my method works:
Given: 
$$\ a∝b∝c$$
Inverse percentage of a,b,c with this formula is:
$$\frac{100bc}{ab+ac+bc}+\frac{100ac}{ab+ac+bc}+\frac{100ab}{ab+ac+bc}$$
I've been out of college for 30 years and am a bit rusty with some math.  I would appreciate anyone validating my method and providing a simpler formula for calculating inverse proportions with 5 or more variables.
Thank you.
 [/INST] I am not too sure precisely what you are trying to do, but it seems you want to extend $100\dfrac{\frac{1}{a}}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}=\dfrac{100bc}{ab+ac+bc}$ and $\dfrac{100bc}{ab+ac+bc}+\dfrac{100ac}{ab+ac+bc}+\dfrac{100ab}{ab+ac+bc}=100$
For five terms this would be 
$$ 100\dfrac{\frac{1}{a}}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}+\frac{1}{e}}= \dfrac{100bcde}{abcd+abce+abde+acde+bcde}$$
and
$$\dfrac{100bcde}{abcd+abce+abde+acde+bcde} + \dfrac{100acde}{abcd+abce+abde+acde+bcde} \\+ \dfrac{100abde}{abcd+abce+abde+acde+bcde} + \dfrac{100abce}{abcd+abce+abde+acde+bcde} \\+ \dfrac{100abcd}{abcd+abce+abde+acde+bcde}=100$$
It could be wise not to allow scores of $0$
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