# How to find percentage that is inversely proportional to other numbers

This is probably an easy question to answer but it has be stumped. Assume

$$s1 = 40$$ $$s2 = 30$$ $$s3 = 20$$ $$C = s1 + s2 + s3$$ I'm trying to find a percentage for each of those which is the inverse of this number relative to $C$. If the numbers were directly and not inversely proportional to $C$, I would calculate them simply as $S_i/C$. I need the smaller numbers to have a larger percentage so what I'm doing (which is probably wrong) to get the inverse is $100 - \frac{(C - S1* ) * 100}{C}$ which results in 44. However this doesn't make sense because if I do the same thing to $s2$ and $s3$, I'll get numbers that add up to more than 100.

I feel like I'm missing something that's right in front of me but I can't figure out what it is.

• Where are you getting the constraint of that each item's percentage must be the inverse of the total C? – electronpusher May 2 '17 at 19:48
• This is just part of power problem I'm trying to solve. Basically $S_i$ represents how much it costs to generate 1 MWh of power by the source and my assumption is that all sources have to be working so I'm trying to prioritize the cheaper sources by giving them a higher percentage. – ninesalt May 2 '17 at 19:50
• I have doubts about whether what you say you want to do is what you ought to do. The cheapest cost is when all power is produced by the cheapest source, unless there are constraints that prevent this--and if there are, you change the distribution just enough to satisfy the constraint. For example, if something very bad will happen if the share of the most expensive power source is less than 1%, then produce 1% of your power from that source. – David K May 2 '17 at 20:05
• The equation $C=s_1+s_2+s_3$ also seems misleading. What is its purpose? The way you have set it up, $C$ is the total cost of an equal mix of one unit of power from each of the three sources, but you say you want to prioritize the cheapest source, so the mix should not be equal. Hence this seems to be the wrong equation for this application. (This is not to cast doubt on the answer you received; the answer is correct for this question; it is the question I wish to cast doubt upon.) – David K May 2 '17 at 20:08
• The point of $C$ is only so that I can find a ratio between an $S_i$ relative to the total cost so I can just choose the cheapest. Maybe the question's phrasing was a little vague, I apologize. – ninesalt May 2 '17 at 20:17

How about taking the inverse of each $s$, adding them up to get $C'$, then dividing each item $s$ by the total $C'$ to get each item's percentage contribution? I'm not sure if it's clear exactly what you're trying to achieve. Does this data reflect a physical situation?
• Yes, check my comment above. I just tried your approach but in this case $C' = 0.108$ so if you divide any $S$ by that number you get a number larger than 100. – ninesalt May 2 '17 at 19:54
• If I understand the answer correctly, you don't divide $s_i$ by $C',$ you divide $1/s_i$ by $C'.$ – David K May 2 '17 at 19:55