document.write( "Question 586667: 1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the orginal fraction \n" ); document.write( "
Algebra.Com's Answer #373894 by ankor@dixie-net.com(22740)\"\" \"About 
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1: twice the numerator of a fraction exceeds the denominator by 2.
\n" ); document.write( " if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3.
\n" ); document.write( "find the original fraction.
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement
\n" ); document.write( ":
\n" ); document.write( "\"twice the numerator of a fraction exceeds the denominator by 2\"
\n" ); document.write( "2n = d + 2
\n" ); document.write( "or
\n" ); document.write( "d = (2n-2)
\n" ); document.write( ":
\n" ); document.write( "\"if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3\"
\n" ); document.write( "\"%28n%2B1%29%2F%28d%2B1%29\" = \"2%2F3\"
\n" ); document.write( "Cross multiply
\n" ); document.write( "2(d+1) = 3(n+1)
\n" ); document.write( "2d + 2 = 3n + 3
\n" ); document.write( "2d = 3n + 3 - 2
\n" ); document.write( "2d = 3n + 1
\n" ); document.write( "Replace d with (2n-2)
\n" ); document.write( "2(2n-2) = 3n + 1
\n" ); document.write( "4n - 4 = 3n + 1
\n" ); document.write( "4n - 3n = 1 + 4
\n" ); document.write( "n = 5 is the numerator
\n" ); document.write( "and
\n" ); document.write( "d = 2(5) - 2
\n" ); document.write( "d = 8 is the denominator\r
\n" ); document.write( "\n" ); document.write( ":
\n" ); document.write( "\"5%2F8\" is the original fraction
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this; add 1 to the the numerator and the denominator
\n" ); document.write( "\"6%2F9\" reduces to \"2%2F3\"
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