document.write( "Question 663080: The denominator of a fraction exceeds the numerator by 7. If the numerator is increased by three and the denominator increased by 5, the resulting fraction is equal to 1/2. Find the original fraction. \n" ); document.write( "
Algebra.Com's Answer #412617 by ReadingBoosters(3246)\"\" \"About 
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x = numerator
\n" ); document.write( "y = denominator
\n" ); document.write( "x = y+7
\n" ); document.write( "(x+3)/(y+5) = 1/2
\n" ); document.write( "Substitute x into the second equation
\n" ); document.write( "((y+7)+3)/(y+5) = 1/2
\n" ); document.write( "(y + 10) / (y + 5) = 1/2
\n" ); document.write( "Multiply both sides by (y+5)
\n" ); document.write( "y+10 = (y+5)/2
\n" ); document.write( "Multiply both sides by 2
\n" ); document.write( "2(y+10) = y+5
\n" ); document.write( "Distribute the 2
\n" ); document.write( "2y + 20 = y + 5
\n" ); document.write( "Group like terms
\n" ); document.write( "2y - y = 5 - 20
\n" ); document.write( "Combine like terms
\n" ); document.write( "y = -15
\n" ); document.write( "x = y+7 = -15+7 = -8
\n" ); document.write( "The original fraction is -8/-15
\n" ); document.write( "Proof
\n" ); document.write( "-8+3 = -5 and -15 + 5 = -10
\n" ); document.write( "-5/-10 = 1/2
\n" ); document.write( "..................
\n" ); document.write( "Delighted to help.
\n" ); document.write( "-Reading Boosters
\n" ); document.write( "Wanting for others what we want for ourselves. \n" ); document.write( "
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