Hey guys here I am again. Sorry for the double post, but I consider this post had to be separate from the last one. I've already found the answers to the 332-232 problem, suffice to say that lestatdark is right with 5, 13, 17 and 97. However, I won't post the solution yet, maybe some of you (twesterm, lingyis) can find the answers with the correct mathematical procedure, without the use of a calculator.
Also, keep in mind that that problem is one of the 10 problems that were tested in the finals of the Ecuadorian Math Olympiads, along with the M/N one. Good luck trying to answer!
If the procedure hasn't been posted until tomorrow night, I'll post my answer, deal?
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On another note, remember mathematics also includes geometry problems, and I have a few of them I'd like to share with you, but first I need to know how do I copy an image on a Word document, so I can post it here? If you tell me, you'll be getting a few geometry problems from me ;)
Edit:
lestatdark you're right! Congratulations! For that problem, mathematical procedure isn't needed, as long as you got the answer right, simply because it's too hard to write it all. But for the powers one, a mathematical procedure is required because otherwise I can tell you're cheating. Also factorization is the right way to do it. The only fault I find in your procedure is the use of a calculator to determine 332-232, after that what you're doing is obviously right.
Your answer is completely right, and here I'll post the procedure you mentally must have done.
Let b be the number of fruits in a good state and d the number of fruits in a bad state. Since we're talking about fruits, the fractions must be fractions of natural numbers, and the fractions themselves must be natural numbers too. We also have the following equations given to us by the problem:
b=ab+ob , where ab represents the apples in good state and ob represents the oranges in a good state. We also know 1/11b=ob.
d=ad+od , where ad represents the apples in a bad state and od represents the oranges in a bad state. We also know 1/5d=ad.
b+d=100
Now, since all numbers must be natural, then b is a multiple of 11 and d is a multiple of 5. Then we have
b=100-d , and since both 100 and d are multiples of 5, then b must be a multiple of 5 too. Then, b is both a multiple of 11 and 5, and it must also be lower than 100. The only number satisfying the condition is 55. So b=55, and then we know d=45, which is the value we were looking for.
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Come on guys you should try posting problems too!
