SOLUTION: The will of an eccentric millionaire reads as follows: "In the following order, i leave 4/17 of my estate to my son, then 7/13 of the remainder to my wife, then 2/3 of the remainde

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Question 306783: The will of an eccentric millionaire reads as follows: "In the following order, i leave 4/17 of my estate to my son, then 7/13 of the remainder to my wife, then 2/3 of the remainder to my daughter, and the remaining $2 million to my dog." What was the total amount of the millionaire's estate?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The will of an eccentric millionaire reads as follows:
"In the following order, i leave 4/17 of my estate to my son, then 7/13 of the remainder to my wife,
then 2/3 of the remainder to my daughter, and the remaining $2 million to my dog.
" What was the total amount of the millionaire's estate?
:
Let t = amt in the estate (in millions of dollars)
:
Son = 4%2F17t
then
remainder = 13%2F17t
:
wife = 7%2F13 * 13%2F17t
wife = 91%2F221t
then
remainder = 130%2F221t
:
daughter = 1%2F3 * 130%2F221t
daughter = 130%2F663t
:
t = 4%2F17t + 91%2F221t + 130%2F663t + 2
common denominator: 663
t = 156%2F663t + 273%2F663t + 130%2F663t + 2
:
t = 559%2F663t + 2
:
t - 559%2F663t = 2
:
104%2F663t = 2
:
t = 2(663%2F104)
t = 12.75 million dollars