document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #615219 by Theo(13342) $\"\"$ $\"About$

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?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "let x = the sum of money.
\n" ); document.write( "he gave half the money to the first child.
\n" ); document.write( "this means he gave 1/2 * x to the first child and he had 1/2 * x left.
\n" ); document.write( "he gave 2/3 of what he gave to the first child to the second child.
\n" ); document.write( "this means he gave 2/3 * 1/3 * x to the second child = 2/6 * x to the second child.
\n" ); document.write( "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.
\n" ); document.write( "he is left with 1/6 * x which he gave to the third child.
\n" ); document.write( "the third child received 5000.
\n" ); document.write( "1/6 * x = 5000.
\n" ); document.write( "x = 6 * 5000 = 30000.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "let's see if the numbers check out.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "he was left with 15,000 - 10,000 = 5,000
\n" ); document.write( "he gave this to the third child.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the numbers check out and so the solution is assumed to be good.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the following table summarizes the transactions:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "the man          his first child       his second child     his third child.\r\n" );
document.write( "\r\n" );
document.write( "he starts with:\r\n" );
document.write( "\r\n" );
document.write( "30,000\r\n" );
document.write( "\r\n" );
document.write( "he give half of what he has to his first child:\r\n" );
document.write( "\r\n" );
document.write( "15,000           15,000\r\n" );
document.write( "\r\n" );
document.write( "he gives two thirds of what he has left to his second child:\r\n" );
document.write( "\r\n" );
document.write( "5,000            15,000                10,000\r\n" );
document.write( "\r\n" );
document.write( "he gives the rest to his third child:\r\n" );
document.write( "\r\n" );
document.write( "0                15,000                10,000               5,000\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );