It's been a while since algebra class and I've exhausted by google-foo here. How do I get x and k on a side by themselves AND only on one side? I get to a certain point and it feels like I'm missing some important rule.
$$s = \frac{(m + rx)}{k}$$
First step could be multiply both sides by k:
$$sk = m + rx$$
then divide both sides by x, but it doesn't seem to get rid of x on the right side because of m.
$$\frac{sk}{x} = \frac{m}{x} + r$$
What I'm looking for is something to the effect of:
$$xk = m,r,s$$
Edited
What I'm really trying to do is derive a value for x or k when m, r, and s are known, x is an unknown constant, and k is an unknown variable.
Given: $$s = \frac{(m + rx)}{k}$$
I have a series of values:
$$(m1, r1, s1) = (100, 50, 480)$$ $$(m2, r2, s2) = (110, 60, 340)$$ $$(m3, r3, s3) = (35, 90, 3701)$$
x is an unknown constant.
k is a different unknown random number in each set
$$k1 = 13$$ $$k2 = 22$$ $$k3 = 3$$
To derive x, I was thinking that if I could know a product of x*k, something like: $$xk = m,r,s$$
Which in this example yields:
$$xk1 = 1599$$ $$xk2 = 2706$$ $$xk3 = 369$$
From that I can determine the greatest common divisor which produces x:
$$x = 123$$
Any ideas about how I can approach this?