Five Bags of NutsDate: 04/17/2002 at 16:33:43 From: Candy De Loera Subject: The Bag of Nuts George Crackham put five paper bags on the breakfast table. On being asked what they contained, he said: "Well, I have put a hundred nuts in these five bags. In the first and second there are altogether fifty-two nuts; in the second and third there are forty-three; in the third and fourth, thirty-four; in the fourth and fifth, thirty." How many nuts are there in each bag? Date: 04/17/2002 at 17:05:21 From: Doctor Ian Subject: Re: The Bag of Nuts Hi Candy, Here are the bags, with the combined sums: 43 30 _________ _________ / \ / \ [ a ] [ b ] [ c ] [ d ] [ e ] \_________/ \_________/ 52 34 Translating to equations, we get a + b = 52 b + c = 43 c + d = 34 d + e = 30 That looks like a mess, doesn't it? However, let's look at that fourth equation. We can rewrite it this way: d = 30 - e Why do we care? Because this means that we can substitute for d in the third equation: c + d = 34 c + (30 - e) = 34 c = 34 - (30 - e) = 34 - 30 + e = 4 + e And now we can substitute for c in the second equation, and if you keep going, eventually you can find all the other variables in terms of e. How does that help you? Remember, all the bags add up to 100 nuts. So that gives us one final equation: a + b + c + d + e = 100 If you substitute in this equation for all the other variables, e.g., a + b + [4 + e] + [30 - e] + e = 100 you'll end up with a single equation with one variable: e. Solve for e, and you can find the value of all the other variables. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 04/19/2002 at 18:59:28 From: Candy De Loera Subject: The Bag of Nuts Dear Dr. Math, Yes, the equation did help. The only thing that was used to solve the equation was a lot of substitution and simple algebra. It was quite useful because I saw how you interpreted the word problem into an equation that I could apply to other similsr problems in the future. Thank you very much. :) Sincerely, Candy De Loera |
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