document.write( "Question 1164140: The difference of two unit fractions is one third of their sum. Find ratio of the larger fraction to smaller fraction ....A fraction sum .. \n" ); document.write( "

Algebra.Com's Answer #788432 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "In this problem, the word $\"highlight%28unit%29\"$ is excessive.\r
\n" ); document.write( "\n" ); document.write( "Mentioning that the numbers are fractions, is excessive, too.\r
\n" ); document.write( "\n" ); document.write( "The correct formulation is THIS :\r
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document.write( "    The difference of two numbers is one third of their sum. \r\n" );
document.write( "    Find the ratio of the larger number to the smaller one.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In this formulation, the solution is as follows.\r
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document.write( "Let x be the greater number, while \"y\" be the smaller number.\r\n" );
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document.write( "Then the condition says\r\n" );
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document.write( "    x - y = .\r\n" );
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document.write( "Multiply both sides by 3 and simplify\r\n" );
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document.write( "    3x - 3y = x + y.\r\n" );
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document.write( "    3x - x = 3y + y\r\n" );
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document.write( "    2x     = 4y\r\n" );
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document.write( "It implies\r\n" );
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document.write( "     =  = 2.\r\n" );
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document.write( "ANSWER.  Under the given conditions, the ratio of the larger number to the smaller is 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The post-solution note:\r
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document.write( "    The numbers can be rational, irrational, algebraic, transcendent, and even complex.\r\n" );
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document.write( "    The statement remains true in all these cases.\r\n" );
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