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 shared equally among his four younger children. If each of the younger children received #108000; what was the wife's share?
started with m
gave (4/9)m leaving (5/9) m in pocket
gave (2/5)(5/9) m to child = (2/9)m to child leaving 5/9-2/9 = (1/3) m in pocket
gave (1/3)(1/4)m to each child = (1/12)m = #108000
m = 12 * #108000
now the wife got (4/9) of m
answer pls
To find the wife's share, we need to work backwards and find the total amount of money that the man left.
Let's assume the total amount of money the man had was X.
According to the information given, the man left 4/9 of his money to his wife. Therefore, the wife's share is (4/9) * X.
The remainder after giving the wife her share is (1 - 4/9) * X, which simplifies to (5/9) * X.
The man then left 2/5 of this remainder to his eldest child. So, the eldest child's share would be (2/5) * (5/9) * X.
The remaining amount after giving the eldest child his share is (1 - 2/5) * (5/9) * X, which simplifies to (3/5) * (5/9) * X.
This remaining amount is then shared equally among the four younger children. So, each of the four younger children would receive (1/4) * (3/5) * (5/9) * X.
According to the given information, each of the younger children received $108,000. Therefore, we can set up the equation:
(1/4) * (3/5) * (5/9) * X = $108,000.
To solve this equation, we can first simplify the fraction, then multiply both sides by the reciprocal of the fraction to isolate X:
(1/4) * (3/5) * (5/9) * X = $108,000
(3/20) * (5/9) * X = $108,000
X = ($108,000) * (20/3) * (9/5)
Solving this expression will give us the total amount of money the man had (X).
Finally, we can calculate the wife's share by multiplying the total amount of money (X) by (4/9):
Wife's share = (4/9) * X
By plugging in the value of X, we can find the wife's share.