A shopkeeper allows people to buy a cold drink bottle in exchange for five empty bottles. A guy had a party at home and spent 77 cold drink bottles at the party. Now he has 77 empty bottles with him.
How many bottles do you think he can buy in exchange for those 77 empty bottles?
* Lets say y = x
* Multiply through by x xy = x2
* Subtract y2 from each side xy - y2 = x2 - y2
* Factor each side y(x-y) = (x+y)(x-y)
* Divide both sides by (x-y) y = x+y
* Divide both sides by y y/y = x/y + y/y
* And so... 1 = x/y + 1
* Since x=y, x/y = 1 1 = 1 + 1
* And so... 1 = 2