SOLUTION: A man made a will 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

Question 1198175: A man made a will 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 N108 000, what was his wife's share?
Found 3 solutions by math_tutor2020, greenestamps, MathTherapy:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answer: N576000

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Explanation:

Draw 9 rectangles side by side.
Shade exactly 4 of them to represent 4/9 of the money going to the wife.
The remaining 9-4 = 5 unshaded rectangles is the amount left over.

2/5 of those unshaded rectangles is then marked with X to signal this amount of money going to the eldest child.
In other words, you would have 2 unshaded rectangles marked with X.

There are 5-2 = 3 rectangles left over that aren't shaded nor have an X in them.
This is out of the 9 rectangles total.
3/9 = 1/3 of the total money is to be split equally among the four younger children.

Now we'll start another diagram.
Draw a grid of squares that have 3 rows and 4 columns.

The row count is from the denominator in 1/3.
The column count (4) is the number of younger kids we're splitting the remaining money with.
There are 3*4 = 12 inner cells.
This means each of the four remaining kids get 1/12 of the total money.
Imagine that each of the four kids only grabs the first row of cells from that second diagram.

Note how
4*(1/12) = 4/12 = 1/3

We're told that each of those four kids got N108000

If x is the total, then,
1/12 of total = 108000
1/12 of x = 108000
(1/12)*x = 108000
x/12 = 108000
x = 108000*12
x = 1296000

The total amount of money is N1296000

Take 4/9 of this to find the wife's share
(4/9)*1296000 = 576000

After she gets her share, there's 1296000-576000 = 720000 left over.
2/5 of this remaining amount is for the eldest, so (2/5)*720000 = 288000 goes for the oldest. Which leaves 720000-288000 = 432000 for the four other kids.
Or you could say 3/5 of 720000 = (3/5)*720000 = 432000 is to be split equally among the four other younger children
432000/4 = 108000
We have confirmed the answer.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

(1) The wife gets 4/9 of the money; 5/9 of it is left.

(2) The eldest child gets 2/5 of the money that is left; that is (2/5) of (5/9) of the whole amount: (2/5)(5/9)=2/9. Now the fraction of the whole amount left is 5/9-2/9 = 3/9 = 1/3.

(3) Each of the other four children gets 1/4 of what is left. (1/4) of (1/3) of the whole amount is 1/12 of the whole amount.

It is given that each of those younger children got N108,000, so the whole amount was 12*N108,000 = N1,296,000.

The wife's share was 4/9 of the total: (4/9)(N1,296,000) = N576,000.

ANSWER: N576,000

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

man made a will 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 N108 000, what was his wife's share?

With going to his wife, remains With of the REMAINDER going to the eldest child, remains With to be shared equally among his 4 younger children, . Each of the 4 younger children received of the money. With W being the wife's share, we now get the following proportion: 3W = 16(108,000) ------ Cross-multiplying Wife's share, or

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