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

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(13198)   (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.

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

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

The wife's share is $576,000.

Answer by josgarithmetic(39616)   (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.

You can solve for t, but the question asks for .
Answer by MathTherapy(10551)   (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:
Fraction eldest child received:
Fraction ALL four younger children received:
Fraction each of the four younger children received:
With each of the four younger children receiving , or $108,000, and the wife's share being W, we get the following PROPORTION and wife's (W's) share:
RELATED QUESTIONS
A man made a will in which he left 4/9 of his money to his wife and 2/5 of the remainder... (answered by math_tutor2020,greenestamps,MathTherapy)
In his will a man leaves one half of his money to his wife, one half of what is then left (answered by solver91311)
In his will, a man leaves one-half of his money to his wife, one-half of what is left to... (answered by sdmmadam@yahoo.com)
A man was on his deathbed, and wanted to settle his estate with a will. His estate... (answered by JulietG)
A man gave two fifths of his paycheck to his wife and spent half of the remainder. If he (answered by subudear)
A man left 3/7 of his money to his wife,1/2 of the remainder to his brother and the rest... (answered by mananth)
A man left 3/7 of his money to his wife, 1/2 of the remainder to his brother and the rest (answered by josmiceli)
A man gave 1/2 of his money to his brother, 1/6 to his friend and the remainder an amount (answered by JulietG)
A man left $72,000 to his wife and son. The ratio of the wife's share to the son's was... (answered by fractalier)