document.write( "Question 1171419: Hi
\n" ); document.write( "Bob and John had $540.00 altogether. Bob gave 1/7 of his money to John. In return John gave 1/4 of his total amount he had to Bob.Then they had both an equal amount of money.
\n" ); document.write( "How much did Bob have at first.
\n" ); document.write( "My solution is as follows B + J = 540
\n" ); document.write( "6/7B = 3/4J
\n" ); document.write( "upon solving the equation i get Bob $252 & John $288
\n" ); document.write( "however the book says that Bob had $210
\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #850853 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "Bob and John had $540.00 altogether. Bob gave 1/7 of his money to John.
\n" ); document.write( "In return John gave 1/4 of his total amount he had to Bob.
\n" ); document.write( "Then they had both an equal amount of money.
\n" ); document.write( "How much did Bob have at first.
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\n" ); document.write( "\n" ); document.write( " This problem is good to solve it by the BACKWARD method.\r
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document.write( "They started having $540 altogether.\r\n" );
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document.write( "The money did not get out and did not come from outside: they circulated inside.\r\n" );
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document.write( "The problem says that they finished having equal amounts.\r\n" );
document.write( "Hence, at the end, Bob and John had $170, each.\r\n" );
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document.write( "Before it, John gave 1/4 of his total amount he had to Bob.\r\n" );
document.write( "So, John left with 3/4 of the amount he has before it, which is $270\r\n" );
document.write( "Hence, immediately before it, John had   = 360 dollars,\r\n" );
document.write( "and John gave 360/4 = 90 dollars to Bob.\r\n" );
document.write( "Hence, when John had 360 dollars, Bob had 270-90 = 180 dollars.\r\n" );
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document.write( "Thus we completed one step back and found that before Bob gave 1/7 of his money to John,\r\n" );
document.write( "they had $360 (John) and $180 (bob).\r\n" );
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document.write( "Now we know that after Bob gave 1/7 of his money to John, Bob left with 6/7 of his money, which is $180.\r\n" );
document.write( "Hence, before this giving, Bob's initial money was   = $210.\r\n" );
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document.write( "Hence, John's initial money was $540 - $210 = $330.\r\n" );
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document.write( "ANSWER.  Initially, Bob had $210,  John had $330.\r\n" );
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document.write( "CHECK.   (Bob, John)          (Bob,        John)             (Bob,        John)\r\n" );
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document.write( "         (210, 330)    --->   (210-30=180, 330+30=360)  --->  (180+90=270, 360-90=270).    ! correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved mentally, without using equations, by the BACKWARD method.\r
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