1. The problem statement, all variables and given/known data One hundred bushels of grain are to be distrubuted amongst 100 people. Each man gets 3 bushels, each woman gets 2 bushels, and each child gets 1/2 bushels. How many men, women and children are there? 2. Relevant equations GCD, euclidean algorithm, Diophantine equation 3. The attempt at a solution I'm a bit thrown off, is their an algorithm way to find the answer here? I'm assuming i'm supposed to use the diophantine equation at some point since it's a question from that chapter, but I'm having difficulty finding out how to do it with 3 variables. I tried solving for men in the persons equation and then substituting that value in to the bushel equation, therefore having only 2 variables so I could use the diophanine equation, but i'm starting to think I'm going to need to do this in a guess and check sort of way? I don't mind doing this, it just seems inefficient. If there is an algorithmic way to find the answer I'd like to know it. Anyone care to shed some light?