A man made a will in which he keft 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 #108 000 What was his wife share
1 - 4/9 = 5/9
2/5 of 5/9 = 2/9
1/4 * 2/9 x = 1/18
wife got 4/9 = 8/18 = 8*108000
To find out the wife's share, we need to determine the amount of money left after the bequests to the eldest and younger children.
Let's assume the total amount of money the man left is X.
According to the will:
- The wife receives 4/9 of the money.
- The remainder, after giving 4/9 to the wife, is (1 - 4/9) = 5/9 of X.
- The eldest child receives 2/5 of the remainder (5/9)X.
Therefore, the amount left after giving to the eldest child is:
(5/9)X - (2/5)(5/9)X = (5/9)X - (10/45)X = (25/45)X = (5/9)X.
We also know that the amount left after giving to the four younger children is #108,000, and this amount is shared equally among them.
Let's denote the amount left for the four younger children as Y.
According to the given information, the four younger children receive Y/4 each, which is equal to #108,000.
So, we have the equation:
Y/4 = #108,000.
To solve for Y, we multiply both sides of the equation by 4:
Y = 4 * #108,000.
Calculating Y:
Y = 4 * #108,000 = #432,000.
Now that we know Y, we can find the wife's share by subtracting Y from the amount remaining after giving to the eldest child:
Wife's share = (5/9)X - Y = (5/9)X - #432,000.
Unfortunately, without knowing the actual value of X (the total amount of money the man left), we cannot determine the wife's share accurately.
To find the wife's share, we need to determine the total amount of money the man left behind and how it was divided among the wife, eldest child, and the four younger children.
Let's start by assigning variables:
Let's say the total amount of money left behind by the man is M.
The wife's share would then be (4/9) of M.
The remaining amount after the wife's share is subtracted would be ((9-4)/9) of M, which simplifies to (5/9) of M.
Now we know that the eldest child received (2/5) of the remaining amount, which is (2/5) * (5/9) * M.
The rest, after the wife and eldest child receive their shares, is to be equally divided among the four younger children. We are given that each younger child receives $108,000. So, the total amount for the four younger children is 4 * $108,000.
Therefore, we can set up an equation:
(5/9) * M - (2/5) * (5/9) * M = 4 * $108,000
To solve this equation, we can simplify it as follows:
(5/9) * M - (2/9) * M = 4 * $108,000
(3/9) * M = 4 * $108,000
(1/3) * M = $432,000
To isolate M, we can multiply both sides by 3:
M = 3 * $432,000
M = $1,296,000
Now we can find the wife's share:
Wife's share = (4/9) * M
= (4/9) * $1,296,000
= $572,000
Therefore, the wife's share is $572,000.