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Math Help - Millionaire's Estate

  1. #1
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    Millionaire's Estate

    The will of an eccentric millionaire reads as follows: "I leave 4/17 of my estate to my son, 7/13 of the remainder to my wife, 2/3 of the remainder to my daughter, and the remaining $2 million to my dog." What was the total amount of the estate?
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  2. #2
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    Quote Originally Posted by MathMage89 View Post
    The will of an eccentric millionaire reads as follows: "I leave 4/17 of my estate to my son, 7/13 of the remainder to my wife, 2/3 of the remainder to my daughter, and the remaining $2 million to my dog." What was the total amount of the estate?
    If 4/17 is removed from 1, then what remains is 13/17.
    Can you see that?
    If yes, then we go ahead.

    [If not, then 1 -4/17 = 17/17 -4/17 = 13/17]

    We are asked to find the total amount of the estate, so let x = the total amount of the estate.

    "I leave 4/17 of my estate to my son....
    So what remains is (13/17)x.

    ....7/13 of the remainder to my wife...
    So what remains is (6/13) of the (13/17)x.
    Which simplifies to (6/13)*(13/17)x = (6/17)x.

    ....2/3 of the remainder to my daughter...
    So what remains is 1/3 of the (6/17)x.
    Which simplifies to (1/3)*(6/17)x = (2/17)x.

    ....and the remaining $2 million to my dog."
    That means the (2/17)x is 2,000,000 dollars.
    So,
    (2/17)x = 2,000,000
    x = (2,000,000) / (2/17)
    x = (2,000,000)*(17/2)
    x = 17,000,000 dollars

    Therefore, the total amount of the estate was $17 Million. -----answer.
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