# Reversing a summation algorithum

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:

For example:

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

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?

• 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. Aug 16, 2013 at 21:23
• 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. Aug 16, 2013 at 21:25
• This question might be better suited for math.SE. I have flagged it for migration.
– Bart van Ingen Schenau
Aug 17, 2013 at 11:09

Sum(Cn) = t(Sum(Cn/Sn) + w/100)