document.write( "Question 777864: If 5 is added to the numerator and the denominator of a fraction the value of the result is 5/7. If 5 is subtracted from the numerator and the denominator of the fraction the value of the result is 5/9. What is the fraction? \n" ); document.write( "

Algebra.Com's Answer #474302 by mananth(16946) $\"\"$ $\"About$

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let the fraction be x/y\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B5%29%2F%28y%2B5%29+=5%2F7\"$ \r
\n" ); document.write( "\n" ); document.write( "cross multiply
\n" ); document.write( "7(x+5)=5(y+5)
\n" ); document.write( "7x+35=5y+25
\n" ); document.write( "7x-5y=-10..........................(1)\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-5%29%2F%28y-5%29+=5%2F9\"$ \r
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\n" ); document.write( "\n" ); document.write( "9(x-5)=5(y-5)\r
\n" ); document.write( "\n" ); document.write( "9x-45=5y-25
\n" ); document.write( "9x-5y=20............................(2)\r
\n" ); document.write( "\n" ); document.write( "7 x -5 y = -10 .............1
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\n" ); document.write( "9 x -5 y = 20 .............2
\n" ); document.write( "Eliminate y
\n" ); document.write( "multiply (1)by -1
\n" ); document.write( "Multiply (2) by 1
\n" ); document.write( "-7 x 5 y = 10
\n" ); document.write( "9 x -5 y = 20
\n" ); document.write( "Add the two equations
\n" ); document.write( "2 x = 30
\n" ); document.write( "/ 2
\n" ); document.write( "x = 15
\n" ); document.write( "plug value of x in (1)
\n" ); document.write( "7 x -5 y = -10
\n" ); document.write( "105 -5 y = -10
\n" ); document.write( " -5 y = -10 -105
\n" ); document.write( " -5 y = -115
\n" ); document.write( " y = 23 \r
\n" ); document.write( "\n" ); document.write( "15/23\r
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