document.write( "Question 951408: If 5 is added to both the numerator and the denominator of a fraction the resut is 4/7. If 1 is subtractedfrom both the numerator and denominator the resut is 2/5. Find the fraction. \n" ); document.write( "

Algebra.Com's Answer #581004 by Fombitz(32388) $\"\"$ $\"About$

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Let the fraction be $\"X%2FY\"$
\n" ); document.write( " $\"%28X%2B5%29%2F%28Y%2B5%29=4%2F7\"$
\n" ); document.write( " $\"4%28Y%2B5%29=7%28X%2B5%29\"$
\n" ); document.write( " $\"4Y%2B20=7X%2B35\"$
\n" ); document.write( "1. $\"-7X%2B4Y=15\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"%28X-1%29%2F%28Y-1%29=2%2F5\"$
\n" ); document.write( " $\"5%28X-1%29=2%28Y-1%29\"$
\n" ); document.write( " $\"5X-5=2Y-2\"$
\n" ); document.write( "2. $\"5X-2Y=3\"$
\n" ); document.write( "Multiply eq. 2 by 2 and add to eq. 1,
\n" ); document.write( " $\"-7X%2B4Y%2B10X-4Y=15%2B6\"$
\n" ); document.write( " $\"3X=21\"$
\n" ); document.write( " $\"X=7\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"5%287%29-2Y=3\"$
\n" ); document.write( " $\"35-2Y=3\"$
\n" ); document.write( " $\"-2Y=-32\"$
\n" ); document.write( " $\"Y=16\"$
\n" ); document.write( " \n" ); document.write( "

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