document.write( "Question 701059: Find a fraction that reduces to 3/4 either if 1 is added to the numerator or if 11 is subtracted from the numerator and the denominator is halved. \r
\n" ); document.write( "\n" ); document.write( "Please help!
\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #432208 by DrBeeee(684) $\"\"$ $\"About$

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Let your fraction be a/b.
\n" ); document.write( "Then we have
\n" ); document.write( "(1) (a+1)/b = 3/4 and
\n" ); document.write( "(2) (a-11)/(b/2) = 3/4 which simplifies to
\n" ); document.write( "(3) 2*(a-11)/b = 3/4
\n" ); document.write( "Since (1) and (3) equal the same number, 3/4, we can set them equal to each other and get
\n" ); document.write( "(4) (a+1)/b = 2*(a-11)/b
\n" ); document.write( "In (4) the b cancels from each side (assuming b is not zero) leaving
\n" ); document.write( "(5) a+1 = 2a-22 or
\n" ); document.write( "(6) a = 23
\n" ); document.write( "Use a of (6) in (1) and get
\n" ); document.write( "(7) (23+1)/b = 3/4 or by cross miultiplying we get
\n" ); document.write( "(8) 3b = 4*24 or
\n" ); document.write( "(9) b = 32
\n" ); document.write( "Let's check the values of a and b using (2).
\n" ); document.write( "Is ((23-11)/(32/2) = 3/4)?
\n" ); document.write( "Is (12/16 = 3/4)?
\n" ); document.write( "Is (3/4 = 3/4)? Yes
\n" ); document.write( "Answer: The fraction is 23/32. \n" ); document.write( "

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