S.O.S. Mathematics CyberBoard

This problem is one in which we know the solution to the formula itself, we know the integers, and we know the variables, however we only know a few of the equations. I'm not positive in what sort of mathematics will be used to solve this, however I know that the solution is actually quite simple and involves few functions, however the data required to figure out the exact formula is massive. The real issue with this problem is that each set of integers have multiple outputs and where exactly the outputs are going is unknown but you know that they are using a percentile for each split.

Basically the problem looks like this, I will actually add the numbers in in a second post:

<var1> g*(var1)=a h*(var1)=b i*(var1)=c <var2> j*(var2)=d k*(var2)=e l*(var2)=f
<var3> m*(var3)=s n*(var3)=t o*(var3)=u <var4> p*(var4)=v q*(var4)=w r*(var4)=x

this is where we begin to not know some of the equations( double letters are new integers not a*a for example):

e-[(a-f)*((?)%)]=aa w-[(s-x)*((?)%)]=bb
b-[(d-c)*((?)%)]=cc t-[(v-u)*((?)%)]=dd

(this is where I wtf:)
e-[(a-f)*((??)%)]=ee w-[(s-x)*((??)%)]=ff
b-[(d-c)*((??)%)]=gg t-[(v-u)*((??)%)]=hh

Then The problem is givin in a order that is unknown, meaning each different part of the equations is solved in a certain order one after the other and not simultaneously. ANd somehow (i know I'm missing a step to the problem which wis why I'm having so much trouble) it winds up with this kind of answer:

<var1>-(cc+gg)=<new1> <var2>-(aa+ee)=<new2>
<var3>-(dd+hh)=<new3> <var4>-(bb+hh)=<new4>

Another problem figuring out this formula is that there are not always the same number of beginning variables and the second set of functions do not always apply to the same other variables but the functions do happen. Perhaps it will make more sense when I put real numbers into it.

It's not very inspiring to look at a page of forumulas and harbor the suspicion that they are something some sadistic instructor decided to make up or that they are a product of years of institutionalized rigor designed to weed out all but the most qualified candidates from the limited number of professional positions available in some economically struggling nation ( perhaps the US, nowadays). This would be so much more interesting if you could explain some reason that this problem arises. Is it from crypttography or something like that?