document.write( "Question 44249: Please help me solve this problem:\r
\n" ); document.write( "\n" ); document.write( "If the numerator of a fraction is increased by 6 and the denominator is decreased by 5, the resulting fraction is 3/4.If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. Find the original fraction.\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #29230 by venugopalramana(3286)\"\" \"About 
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If the numerator of a fraction is increased by 6 and the denominator is decreased by 5, the resulting fraction is 3/4.If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. Find the original fraction.
\n" ); document.write( "LET ORIGINAL FRACTION =N/D
\n" ); document.write( "N.R. S INCREASED BY 6 ...HENCE NEW N.R. =N+6
\n" ); document.write( "D.R. IS DECREASED BY 5...NEW D.R. IS ....=D-5
\n" ); document.write( "FRACTION IS
\n" ); document.write( "(N+6)/(D-5)=3/4
\n" ); document.write( "4(N+6)=3(D-5)
\n" ); document.write( "4N+24=3D-15
\n" ); document.write( "3D-4N=39..............................I
\n" ); document.write( "RECIPROCAL OF ORIGINAL FRACTION =D/N
\n" ); document.write( "REDUCED BY 1 ....D/N -1 =(D-N)/N=16/9
\n" ); document.write( "9(D-N)=16N
\n" ); document.write( "9D-9N=16N
\n" ); document.write( "9D-25N=0...............II
\n" ); document.write( "EQN.I*3-EQN.II GIVES
\n" ); document.write( "9D-12N-9D+25N=117
\n" ); document.write( "13N=117
\n" ); document.write( "N=117/13=9
\n" ); document.write( "3D-4*9=39
\n" ); document.write( "3D=39+36=75
\n" ); document.write( "D=75/3=25
\n" ); document.write( "HENCE ORIGINAL FRACTION IS 9/25 \n" ); document.write( "
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