I am coding something in Ruby and I came across this math problem. I have a system of equations and inequalities that looks like this:
$$ a = \sum \frac{a_n * x_n}{100}\\ b = \sum \frac{b_n * x_n}{100}\\ c = \sum \frac{c_n * x_n}{100} $$
And for every $x_n$ I have:
$$ \text{min}x_n < x_n < \text{max}x_n $$
There can be random numbers of $x$ and these equations. But let's say that it won't be larger than $10$:
$$ n \leq 10 $$
I know all values, but $x_n$. Is there a way of calculating each $x_n$? Or at least get a narrower range for them?