I am trying to get Mathematica to solve the following equality in terms of $w_i$
$\displaystyle \frac{\sum_{i = 1}^{n} x_i }{\sum_{i = 1}^{n} y_i} = \frac{\sum_{i = 1}^{n} ( (\frac{x_i}{y_i}) w_i ) }{n} $
(Background: https://math.stackexchange.com/questions/137332/relationship-between-ratios-and-averages-of-ratios)
But it's telling me "This system cannot be solved with the methods available to Solve."
Now, I'm guessing this is because I haven't given Mathematica enough information about my assumptions (specifically, that $w_i$ is expressible as a function of $x_i$ and $y_i$, or something similar)
What am I doing wrong here, and how would I go about using Mathematica to solve equalities like these?
Solve[Sum[Subscript[x, i],
{i, 1, n}]/
Sum[Subscript[y, i],
{i, 1, n}] ==
Sum[(Subscript[x, i]/
Subscript[y, i])*
Subscript[w, i],
{i, 1, n}]/n,
Subscript[w, i]]
PS.) I realize my title stinks... I blame myself for not even knowing enough about what my problem is to give this question a cogent title. If someone could Edit the question and give it a real title and/or suggest one, I'd be appreciative.
w_i
as a single symbol, and it doesn't know that it's related tow_1, w_2, ...
. $\endgroup$n
first. I know my comment is not an answer, that's why I wrote it as a comment. $\endgroup$