Question 1150819
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There are, as usual, many different ways to set up this problem for solving.  I hope you will get responses from other tutors showing different methods; perhaps you will find a method different than mine more to your liking.<br>
Let x be the full amount of money.<br>
total amount: x<br>
The wife gets 4/9 of the money; 5/9 is left for the children.<br>
wife's share: (4/9)x
children's share: (5/9)x<br>
The eldest child get 2/5 of what is left for the children; 3/5 of what is left goes to the other children.<br>
eldest child's share: (2/5)(5/9)x = (2/9)x
remaining children's shares: (3/5)(5/9)x = (3/9)x = (1/3)x<br>
What remains for the four youngest children is divided equally among them.<br>
share for each younger child: (1/4)(1/3)x = (1/12)x<br>
The share for each younger child is $108,000.<br>
{{{(1/12)x = 108000}}}
{{{x = 1296000}}}<br>
The total amount of money is $1,296,000.<br>
The wife's share is 4/9 of the total:<br>
{{{(4/9)(1296000) = 4(144000) = 576000}}}<br>
The wife's share is $576,000.<br>