document.write( "Question 1036683: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the original fraction? \n" ); document.write( "

Algebra.Com's Answer #651506 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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let n = the numerator of the original fraction
\n" ); document.write( "let d = the denominator
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\n" ); document.write( "Write an equation for each statement
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\n" ); document.write( "The denominator of a fraction is four less than twice the numerator
\n" ); document.write( "d = 2n - 4
\n" ); document.write( ":
\n" ); document.write( "if three is added to both the numerator and denominator, the new fraction is equal to two-thirds.
\n" ); document.write( " $\"%28%28n%2B3%29%29%2F%28%28d%2B3%29%29\"$ = $\"2%2F3\"$
\n" ); document.write( "cross multiply
\n" ); document.write( "3(n+3) = 2(d+3)
\n" ); document.write( "3n + 9 = 2d + 6
\n" ); document.write( "3n = 2d + 6 - 9
\n" ); document.write( "3n = 2d - 3
\n" ); document.write( "replace d = (2n-4)
\n" ); document.write( "3n = 2(2n-4) - 3
\n" ); document.write( "3n = 4n - 8 - 3
\n" ); document.write( "3n - 4n = -11
\n" ); document.write( "-n = -11
\n" ); document.write( "n = 11
\n" ); document.write( "Find d using the 1st equation d = 2n - 4
\n" ); document.write( "d = 2(11) - 4
\n" ); document.write( "d = 18
\n" ); document.write( ":
\n" ); document.write( " What is the original fraction? $\"11%2F18\"$
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\n" ); document.write( ":
\n" ); document.write( "You can check this for yourself, in the statement
\n" ); document.write( "\"if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. \"
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