Re: Math Problem
I eliminate one of the variables because the "oldest child" thing implies that one solution has an oldest child while another does not (hence, the "oldest" and "middle" children must be the same age). I can't immediately eliminate the variable.. I only do that at the end when we get the "oldest child" information.
As for why I know that there are not other sets of three factors whose product is 36 and that add up to X, if there were, then the problem would not have a unique answer. I am assuming, because you ask the question, that there is a unique answer.
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