document.write( "Question 186870: The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to \"1%2F3\". Find the original fraction? How and what do I do to answer the above question? I am really lost on equations like these. Can you help me? \n" ); document.write( "
Algebra.Com's Answer #140092 by Edwin McCravy(20056)\"\" \"About 
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The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to \"1%2F3\". Find the original fraction? How and what do I do to answer the above question? I am really lost on equations like these. Can you help me?
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document.write( "Let N = the numerator\r\n" );
document.write( "Let D = the denominator\r\n" );
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document.write( "Then \r\n" );
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document.write( "Fraction = \"N%2FD\"\r\n" );
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\n" ); document.write( "The ratio of the numerator to the denominator
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document.write( "So\r\n" );
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document.write( "\"N%2FD=1%2F4\"\r\n" );
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\n" ); document.write( "If 3 is added to the numerator and subtracted
\n" ); document.write( "from the denominator, the new fraction reduces to 1/3
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document.write( "\"%28N%2B3%29%2F%28D-3%29=1%2F3\"\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "\"system%28N%2FD=1%2F4%2C%28N%2B3%29%2F%28D-3%29=1%2F3%29\"\r\n" );
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document.write( "Cross multiply the first equation:\r\n" );
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document.write( "\"D=4N\"\r\n" );
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document.write( "Cross multiply the second equation:\r\n" );
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document.write( "\"D-3=3%28N%2B3%29\"\r\n" );
document.write( "\"D-3=3N%2B9\"\r\n" );
document.write( "\"D=3N%2B12\"\r\n" );
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document.write( "Now the system is simply:\r\n" );
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document.write( "\"system%28D=4N%2CD=3N%2B12%29\"\r\n" );
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document.write( "\"4N=3N%2B12\"\r\n" );
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document.write( "\"N=12\"\r\n" );
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document.write( "\"D=3N%2B12=3%2812%29%2B12=36%2B12=48\"\r\n" );
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document.write( "So the original fraction was \"N%2FD=12%2F48\"\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "\"12%2F48\" is in the ratio of 1 to 4 since it reduces to \"1%2F4\"\r\n" );
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document.write( "Now let's add 3 to the numerator 12 and get 15\r\n" );
document.write( "and let's subtract 3 from the denominator 48 and get 45.\r\n" );
document.write( "Then we should have a fraction that reduces to \"1%2F3\"\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "\"15%2F45=1%2F3\"\r\n" );
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document.write( "So we are correct.  The desired fraction is \"12%2F48\"\r\n" );
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document.write( "Edwin

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