document.write( "Question 1201447: The denominator of a fraction is 8 more than the numerator. If both the numerator and denominator are decreased by 5, then the resulting fraction becomes 2/3. Find the original fraction \n" ); document.write( "

Algebra.Com's Answer #835821 by mananth(16946) $\"\"$ $\"About$

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let x be the numerator
\n" ); document.write( "and y be the denominator\r
\n" ); document.write( "\n" ); document.write( "y= x+8
\n" ); document.write( "y-x =8 ................(1)\r
\n" ); document.write( "\n" ); document.write( "Both numerator and denominator decreased by 5\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-5%29%2F%28y-5%29+=2%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "3(x-5) = 2(y-5)\r
\n" ); document.write( "\n" ); document.write( "3x-15 = 2y-10
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\n" ); document.write( "3x-2y=5................(2)\r
\n" ); document.write( "\n" ); document.write( "Multiply equation 1 by 2\r
\n" ); document.write( "\n" ); document.write( "we get
\n" ); document.write( "2y-2x=16 add this equation to 2\r
\n" ); document.write( "\n" ); document.write( "we get
\n" ); document.write( "2y-2x=16
\n" ); document.write( "3x-2y=5
\n" ); document.write( "x=21
\n" ); document.write( "y=x+8\r
\n" ); document.write( "\n" ); document.write( "y = 21+8=29\r
\n" ); document.write( "\n" ); document.write( "Fraction is 21/29\r
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