- #1
PsychonautQQ
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- 10
Homework Statement
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?
Homework Equations
GCD, euclidean algorithm, Diophantine equation
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 into 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?