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?
:
Let t = amt in the estate (in millions of dollars)
:
Son = {{{4/17}}}t
then
remainder = {{{13/17}}}t
:
wife = {{{7/13}}} * {{{13/17}}}t
wife = {{{91/221}}}t
then
remainder = {{{130/221}}}t
:
daughter = {{{1/3}}} * {{{130/221}}}t
daughter = {{{130/663}}}t
:
t = {{{4/17}}}t + {{{91/221}}}t + {{{130/663}}}t + 2
common denominator: 663
t = {{{156/663}}}t + {{{273/663}}}t + {{{130/663}}}t + 2
:
t = {{{559/663}}}t + 2
:
t - {{{559/663}}}t = 2
:
{{{104/663}}}t = 2
:
t = 2({{{663/104}}})
t = 12.75 million dollars