SOLUTION: A man dies and leaves half of his wealth to his wife. He leaves 1/7 of his wealth to his son. He leaves 2/3 of his wealth to his servant and $2,000 to his dog. How much total we

Question 7663: A man dies and leaves half of his wealth to his wife. He leaves 1/7 of his wealth to his son. He leaves 2/3 of his wealth to his servant and $2,000 to his dog. How much total wealth did the man have?
Found 2 solutions by glabow, prince_abubu:
Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
This kind of indeterminate problem usually has constraints. I will use: what is the smallest amount he could have had.
We have the following information

The issue now is to find an integer w that allows a solution. Obviously 42 will work.
The numerator of the distributions is then
So he leaves 1/2 of that to his wife;
He leaves 1/7 of that to his son;
He leaves 2/3 of that to his servant
So his total estate was
[Since I hate these kinds of problems, someone should check my logic carefully.]
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
First of all, the fractions add up too much. 1/2 + 1/7 + 2/3 > 1. In other words, you can't divide your wealth so that the portions are of the size 1/2, 1/7, and 2/3 of the original. Actually, the wife's portion and the servants portion even exceed his wealth, since even 1/2 + 2/3 > 1. There would then be no more left-over for his son and his dog. You might need to check the problem again to get the right figures.
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