Thread: 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?

Originally Posted by MathMage89

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.