Question 996955: A man had a sum of money which he sells among three children. The first took half of the money, the second took 2/3 of what he gave to the first. He the remainder to the third child. If the third removed Ghc5000, how much money did the man shared?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A man had a sum of money which he sells among three children. The first took half of the money, the second took 2/3 of what he gave to the first. He the remainder to the third child. If the third removed Ghc5000, how much money did the man shared?
let x = the sum of money.
he gave half the money to the first child.
this means he gave 1/2 * x to the first child and he had 1/2 * x left.
he gave 2/3 of what he gave to the first child to the second child.
this means he gave 2/3 * 1/3 * x to the second child = 2/6 * x to the second child.
this means he had 1/2 * x - 2/6 * x left which is equal to 3/6 * x - 2/6 * x which is equal to 1/6 * x.
he is left with 1/6 * x which he gave to the third child.
the third child received 5000.
1/6 * x = 5000.
x = 6 * 5000 = 30000.
let's see if the numbers check out.
he gave half of 30,000 to the first the first child which means he gave 15,000 to the first child and was left with 30,000 - 15,000 = 15,000.
he gave 2/3 of what he gave to the first child to the second child which means he gave 2/3 * 15000 to the second child = 10,000.
he was left with 15,000 - 10,000 = 5,000
he gave this to the third child.
the numbers check out and so the solution is assumed to be good.
the following table summarizes the transactions:
the man his first child his second child his third child.
he starts with:
30,000
he give half of what he has to his first child:
15,000 15,000
he gives two thirds of what he has left to his second child:
5,000 15,000 10,000
he gives the rest to his third child:
0 15,000 10,000 5,000
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