SOLUTION: A man made a will the in which he left 4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children

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Question 1150819: A man made a will the in which he left 4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children. If each of the younger children received $108000; what was his wife's share?
Found 3 solutions by greenestamps, josgarithmetic, MathTherapy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

Let x be the full amount of money.

total amount: x

The wife gets 4/9 of the money; 5/9 is left for the children.

wife's share: (4/9)x
children's share: (5/9)x

The eldest child get 2/5 of what is left for the children; 3/5 of what is left goes to the other children.

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

What remains for the four youngest children is divided equally among them.

share for each younger child: (1/4)(1/3)x = (1/12)x

The share for each younger child is $108,000.

%281%2F12%29x+=+108000
x+=+1296000

The total amount of money is $1,296,000.

The wife's share is 4/9 of the total:

%284%2F9%29%281296000%29+=+4%28144000%29+=+576000

The wife's share is $576,000.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
t, the total amount of his money to be distributed

The money to be shared among the four younger children was 432000.

t-4t%2F9-2t%2F9=432000
You can solve for t, but the question asks for 4t%2F9.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A man made a will the in which he left 4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children. If each of the younger children received $108000; what was his wife's share? 
Fraction wife received: 4%2F9

Fraction eldest child received: 

Fraction ALL four younger children received: 

Fraction each of the four younger children received: matrix%281%2C3%2C+%281%2F3%29%2F4%2C+%22=%22%2C+1%2F12%29

With each of the four younger children receiving 1%2F12, or $108,000, and the wife's share being W, we get the following PROPORTION and wife's (W's) share: