document.write( "Question 1189654: Tony and Peter both had some marbles at first. After Tony gave Peter 4/14 of his marbles, the ratio of Tony’s marbles to Peter’s marbles became 5:3. What was the ratio of Peter’s marbles to Tony’s marbles at first? \n" ); document.write( "

Algebra.Com's Answer #821112 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Tony and Peter both had some marbles at first. After Tony gave Peter 4/14 of his marbles,
\n" ); document.write( "the ratio of Tony’s marbles to Peter’s marbles became 5:3.
\n" ); document.write( "What was the ratio of Peter’s marbles to Tony’s marbles at first?.
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\n" ); document.write( "\n" ); document.write( " For me, it is psychologically difficult to see (to read) so long solution for so simple problem.\r
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\n" ); document.write( "\n" ); document.write( " So, I came to bring a shorter solution (thinking that longer solution does not help understanding).\r
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document.write( "Finally, Tony has 5x marbles, while Peter has 3x marbles, where x is the common measure.\r\n" );
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document.write( "Let P = # of marbles Peter had initially;\r\n" );
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document.write( "    T = # of marbles Tony  had initially.\r\n" );
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document.write( "Then we have these equations\r\n" );
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document.write( "    3x = P +     (1)\r\n" );
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document.write( "    5x =        (2)\r\n" );
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document.write( "From equation (2),  x =  = .\r\n" );
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document.write( "Substitute it into equation (1) to get\r\n" );
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document.write( "     = P + .\r\n" );
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document.write( "So,  P =  -  = .\r\n" );
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document.write( "It means that   = .     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "My conception is this: everything which is longer than 5 lines of standard text, is not a Math problem.\r
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\n" ); document.write( "\n" ); document.write( "If a standard/regular school Math problem is given, than its solution should be no longer than 10 - 15 lines of the text; maximum 20 lines.\r
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\n" ); document.write( "\n" ); document.write( "If a problem is exceptional, its solution may require \"more lines\" - it depends and it can be justified.\r
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\n" ); document.write( "\n" ); document.write( "But if the solution to a regular/standard school Math problem is longer than 20 lines, then nobody even will read it . . . \r
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