Dude.
You like math too much.
that's badass, but still.
That is one reason I like math. Because no matter how you are taught something, you can always do it a different way. Math is infinite in how you can achieve something as long as you know the basic relations between numbers.
My teacher once taught us how to do something like this:
You sell x tickets.
y tickets are sold at $5
z tickets are sold at $10
You made $A from the sales
How many of each did you sell?
(of course, x was known and A was known)
I couldn't remember, so I noticed that the prices were a basic ratio, 2:1, and if you sold X tickets, it was simply a matter of applying the ratio.
I noticed this in about 5 minutes, after being completely blanked on a test. I still got docked marks for doing it wrong. Fuckers. I learned more about how to answer that sort of question than anyone else in the class. I learned the fundamental relationship between the price, the profit, and the number of tickets sold.
I could continue on a rant about how school is a perversion of the original idea of learning, but I think not.