document.write( "Question 203140: The difference between the numerator and the denominator of a certain proper fraction is 24. If ⅜ is added to the numerator and ¼ subtracted from the denominator, the value of resulting fraction is 3⁄14. Find the numerator
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Algebra.Com's Answer #153267 by stanbon(75887)\"\" \"About 
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The difference between the numerator and the denominator of a certain proper fraction is 24. If ⅜ is added to the numerator and ¼ subtracted from the denominator, the value of resulting fraction is 3⁄14. Find the numerator
\n" ); document.write( "and denominator.
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\n" ); document.write( "Numerator: x
\n" ); document.write( "Denominator: y
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\n" ); document.write( "Equations:
\n" ); document.write( "x - y = 24
\n" ); document.write( "[x+(3/8)]/[y-(3/14)]=3/14
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\n" ); document.write( "Rearrange the 2nd equation to get:
\n" ); document.write( "[(8x+3)/8]/[(14y-3)/14] = (3/14)
\n" ); document.write( "Invert the left side and multiply to get:
\n" ); document.write( "[14(8x+3)]/[8(14y-3)] = (3/14)
\n" ); document.write( "Cross-multiply to get:
\n" ); document.write( "[14^2(8x+3)] = [24(14y-3)]
\n" ); document.write( "Divide both sides by 24 to get:
\n" ); document.write( "(49/6)(8x+3) = 14y-3
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\n" ); document.write( "Substitute from the 1st equation (y=x-24) to get
\n" ); document.write( "(49/6)(8x+3) = 14(x-24)-3
\n" ); document.write( "(49/6)(8x+3) = 14x -339
\n" ); document.write( "49(8x+3) = 49(14x-339)
\n" ); document.write( "392x+147 = 686x-16611
\n" ); document.write( "16758 = 294x
\n" ); document.write( "x = 57 This is the numerator)
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\n" ); document.write( "Solve for \"y\":
\n" ); document.write( "y = 57-24
\n" ); document.write( "y = 33 (This is the denominator)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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