Question 29035: In his will, a man leaves one-half of his money to his wife, one-half of what is left to his older child, and one-half of what is then left to his younger child. His cousins divide the remainder equally, each receiving $2000. What was the total amount of money in the man's will and how much did his wife and each child get?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! In his will, a man leaves one-half of his money to his wife, one-half of what is left to his older child, and one-half of what is then left to his younger child. His cousins divide the remainder equally, each receiving $2000. What was the total amount of money in the man's will and how much did his wife and each child get?
Let the total amount of money in the man’s will be A$
Amount to wife = (1/2)A
What is left = A-(1/2)A = (1/2) A
Amount to older child = (1/2) of what is left = (1/2)[(1/2)A] = (1/4)A
What is still left = (1/2)A- (1/4)A = (1/4)A
Amount to younger child = (1/2) of what is still left = (1/2)[(1/4)A]=(1/8)A
The remainder left = (1/4)A-(1/8)A= (1/8)A
If there were to be N cousins,then (1/8)A is divided equally amongst the N cousins
and each one’s share =$2000
That is [(1/8)A]/N = 2000
[(1/8)A]=(2000)N
That is (A/8) = 2000 N
Therefore A = (2000 N) X 8
That is A = $16000 N
Answer: The total amonut of money in the man’s will = $(16000 N)
Where N is the total number of cousins of the man.
The wife gets (1/2)A= (1/2)(16000 N) =$ 8000N
Amount to older child = (1/4)A =(1/4)(16000 N) =$ 4000N
Amount to younger child =(1/8)A=(1/8)(16000 N) =$ 2000N
Verification: The sum total of all the shares should be the total amount $A
Therefore: wife’s share + elder child ’s share + younger child ’s share + the cousins’ share
=(1/2)A+(1/4)A+(1/8)A+(1/8)A =A
= $ 8000N+$ 4000N+$2000N+$2000N=$16000N which is correct.
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