document.write( "Question 28256: The denominator of a rational number is 9 less than three times the numerator. The number in simplest form is 3/8. Find the number \n" ); document.write( "
Algebra.Com's Answer #15381 by longjonsilver(2297)\"\" \"About 
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Let the fraction be \"x%2Fy\".\r
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\n" ); document.write( "\n" ); document.write( "We know that y = 3x-9\r
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\n" ); document.write( "\n" ); document.write( "We also know that \"x%2Fy+=+3%2F8\", or 8x = 3y\r
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\n" ); document.write( "\n" ); document.write( "So we have 2 equations:
\n" ); document.write( "3y=8x
\n" ); document.write( "y = 3x-9 --> multiply this by 3, to scale it up:\r
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\n" ); document.write( "\n" ); document.write( "3y=8x
\n" ); document.write( "3y=9x-27\r
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\n" ); document.write( "\n" ); document.write( "Subtracting the 2 equations gives us
\n" ); document.write( "0 = -x+27
\n" ); document.write( "so x=27\r
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\n" ); document.write( "\n" ); document.write( "since x/y is of form 3/8 and we know that x is actually 27, we need to scale the 3 upto 27 (ie multiply by 9), so the 8 needs to be 8*9 --> 72\r
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\n" ); document.write( "\n" ); document.write( "The fraction is 27/72.\r
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\n" ); document.write( "\n" ); document.write( "CHECK: 27*3 = 81
\n" ); document.write( "and 81 less 9 is 72... correct.\r
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\n" ); document.write( "\n" ); document.write( "jon.
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