document.write( "Question 527396: The denominator of a certain fraction is six times the numerator. If 3 is added to the numerator and subtracted from the denominator, the resulting fraction is equivalent to 2/5. Find the original fraction. \n" ); document.write( "
Algebra.Com's Answer #348894 by oberobic(2304)\"\" \"About 
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Define the original fraction as:
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\n" ); document.write( "x/6x
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\n" ); document.write( "Adding 3 to the numerator and the denominator:
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\n" ); document.write( "(x+3)/(6x+3) = 2/5
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\n" ); document.write( "Cross multiply:
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\n" ); document.write( "(x+3) * 5 = (6x+3)*2
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\n" ); document.write( "5x +15 = 12x +6
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\n" ); document.write( "-7x = -9
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\n" ); document.write( "x = 9/7
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\n" ); document.write( "Check the answer:
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\n" ); document.write( "6x = 54/7
\n" ); document.write( "x/6x = (9/7) / (54/7) = 9/7 * 7/54 = 9/54 = 1/6
\n" ); document.write( "That's the correct ratio.
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\n" ); document.write( "9/7+3 = 9/7 + 21/7 = 30/7
\n" ); document.write( "6x+3 = 6*9/7 + 21/7 = 54+21 /7= 75/7
\n" ); document.write( "(x+3)/(6x+3) = (30/7) / (75/7) = 30/7 * 7/75 = 30/75 = 2/5
\n" ); document.write( "Correct.
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\n" ); document.write( "Answer: The original fraction is 9/7.
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\n" ); document.write( "Done. \n" ); document.write( "
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