SOLUTION: One hundred bushels of corn are to be divided among 100 men, women, and children. Men get 3 bushels each. Women get 2 bushels each. Children get 1/2 bushel each. How can the bu

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Question 37394: One hundred bushels of corn are to be divided among 100 men, women, and children. Men get 3 bushels each. Women get 2 bushels each. Children get 1/2 bushel each. How can the bushel be distributed? Is there more than on solution?

I do not have a textbook for this class.
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
We can summarize what we have in two equations:
3M + 2W + (1/2)C = 100 (this is the bushels equation)
M + W + C = 100 (this is the number of people equation)
Since we have three unknowns but just two equations, there should be a number of solutions avalable.
One way to find some of them is to eliminate one variable by linear combination.
I multiplied the top equation by two and subtracted the bottom equation...
6M + 4W + C = 200
M + W + C = 100
yielding
5M + 3W = 100
so that any combination that satisfies this equation solves the problem...for example, eight men and twenty women (leaving 72 children) works...or 14 men, 10 women and 76 children...