If a business charges more for a product than the cost to make it, how is our economy not inevitably doomed for debt? The analogy would be stirring water in a bucket; without adding more water to the bucket, there is no gain... 

Obviously the various resources to create say an iPod came from different countries... but this general concept of x = 4x therefore the company made 3x (as an over simplification) so where did the 3x come from? From people yes, but if it's always subtracting then how do we get to positive?
To continue your example: 
Resources (including labor) cost $x$, product sells for 4$x$. The fat cat business owner makes 3$x$. What does he do with it? If he spends it, for example plays golf or gets his hair done then the people providing those services get the money. Thus there need not be debt, the hairdresser can use these earnings to buy the product the fat cat's business was selling. The usual water analogy is of a circulatory system: water (money) flows from one vessel to the other.