document.write( "Question 437846: If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3/4. Find the original fraction \n" ); document.write( "

Algebra.Com's Answer #302867 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3/4. Find the original fraction
\n" ); document.write( "-----------------------------------------------
\n" ); document.write( "Let the fraction be x/y
\n" ); document.write( "---
\n" ); document.write( "Equations:
\n" ); document.write( "(x-1)/(y-1) = 2/3
\n" ); document.write( "(x+1)/(y+1) = 3/4
\n" ); document.write( "--------
\n" ); document.write( "Rearrange:
\n" ); document.write( "3x-3=2y-2
\n" ); document.write( "4x+4=3y+3
\n" ); document.write( "------------
\n" ); document.write( "Rearrange:
\n" ); document.write( "3x - 2y = 1
\n" ); document.write( "4x - 3y = -1
\n" ); document.write( "----------------------
\n" ); document.write( "Multiply 1st by 3
\n" ); document.write( "Multiply 2nd by 2
\n" ); document.write( "--------
\n" ); document.write( "9x - 6y = 2
\n" ); document.write( "8x - 6y = -2
\n" ); document.write( "-------------------------
\n" ); document.write( "Subtract and solve for \"x\":
\n" ); document.write( "x = 4
\n" ); document.write( "---
\n" ); document.write( "solve for \"y\":
\n" ); document.write( "3x-2y = 1
\n" ); document.write( "12-2y = 1
\n" ); document.write( "2y = 11
\n" ); document.write( "y = 11/2
\n" ); document.write( "---
\n" ); document.write( "Solution: (11/2,4)
\n" ); document.write( "========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

\n" );