document.write( "Question 411917: a fraction has a value 3/4. if 4 is added to its numerator and 8 is subtracted from its denominator, the value of the resulting fraction is 1. what is the original fraction? \n" ); document.write( "

Algebra.Com's Answer #289442 by stanbon(75887) $\"\"$ $\"About$

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a fraction has a value 3/4. if 4 is added to its numerator and 8 is subtracted from its denominator, the value of the resulting fraction is 1. what is the original fraction?
\n" ); document.write( "------
\n" ); document.write( "Equations:
\n" ); document.write( "(x/y) = 3/4
\n" ); document.write( "(x+4)/(y-8) = 1
\n" ); document.write( "-------
\n" ); document.write( "Rearrange:
\n" ); document.write( "4x-3y = 0
\n" ); document.write( "x+4 = y-8
\n" ); document.write( "----
\n" ); document.write( "4x-3y = 0
\n" ); document.write( "x-y = -12
\n" ); document.write( "-----------
\n" ); document.write( "Multiply thru the 2nd equation by 3:
\n" ); document.write( "4x-3y = 0
\n" ); document.write( "3x-3y = -36
\n" ); document.write( "-------------
\n" ); document.write( "Subtract and solve for \"x\":
\n" ); document.write( "x = 36
\n" ); document.write( "----
\n" ); document.write( "Solve for \"y\":
\n" ); document.write( "x+4 = y-8
\n" ); document.write( "36+4 = y-8
\n" ); document.write( "y = 48
\n" ); document.write( "===============
\n" ); document.write( "Original Fraction:
\n" ); document.write( "x/y = 36/48
\n" ); document.write( "========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "============ \n" ); document.write( "

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