Let me get right to the puzzle first:
You are given a budget of $100 to buy 100 pets, choosing at least one of each kind of pet but you must spend every penny on pets. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy?
It doesn't look too hard but when you start to write it out, you may find your self with too many unknowns. This sort of problem is called a Diophantine equation. You will have to finesse a bit of implied information out of the restriction that only whole number solutions are permitted. You would never buy half of a mouse, now would you?
I will post a link to the source of this problem next week because in that same page is the answer and an excellent discussion of the the solution technique and of Diophantine equations in general.
Have fun.
-Prometheus