I have a bit of a math problem on a hobby project of mine, and I was hoping some of the experts here could give me some guidance.

I am preforming some calculations on a set of numbers where the following is true with any given value for w, where:

∑▒C_n/(∑▒〖C_n/S_n +w/100〗)  =t

For example:

Given the set [{C=100,S=47.9},{C=50,S=28.0}], and w=100

[100/([100/47.9]+[50/28.0]+(100/100) )]+[50/([100/47.9]+[50/28.0]+(100/100) )]=30.7794

Except now what I need to do is find w for any given value of t. I know I need to solve for w in the equation somehow, and then it should be simple enough to convert it to code for my algorithm. Unfortunately I am having a bit of trouble with the math involved. I know I did these before in calc, but I can't quite remember it.

Would anyone be able to show me how I would go about solving this problem?

Thanks for your time!

  • 1
    $\begingroup$ The thing to notice though is that denominator is the same in each term, so it can be factored out ofthe sum. A little rearranging of the terms will then get w one side and t, the sum of all the cn and the sum of cn/sn on the other. $\endgroup$ Aug 16, 2013 at 21:23
  • 4
    $\begingroup$ This question appears to be off-topic because it is about a solution to a math problem, and one of interest only to the OP. $\endgroup$ Aug 16, 2013 at 21:25
  • $\begingroup$ This question might be better suited for math.SE. I have flagged it for migration. $\endgroup$
    – Bart van Ingen Schenau
    Aug 17, 2013 at 11:09

1 Answer 1


It's actually just algebra, no calculus involved. The trick is that the denominator is constant, so you can factor it out.

Sum(Cn) = t(Sum(Cn/Sn) + w/100)
Sum(Cn)/t = Sum(Cn/Sn) + w/100
100 * (Sum(Cn)/t - Sum(Cn/Sn)) = w
  • $\begingroup$ You are absolutely right! It looks so much easier when you put it like that. Many thanks! :) $\endgroup$
    – drkstr1
    Aug 16, 2013 at 22:42

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