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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document.write( "and denominator. \n" );
document.write( "
Algebra.Com's Answer #153267 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! 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. \n" ); document.write( "------------------------------ \n" ); document.write( "Numerator: x \n" ); document.write( "Denominator: y \n" ); document.write( "----------------- \n" ); document.write( "Equations: \n" ); document.write( "x - y = 24 \n" ); document.write( "[x+(3/8)]/[y-(3/14)]=3/14 \n" ); document.write( "------------------------- \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 \n" ); document.write( "-------- \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) \n" ); document.write( "-------------- \n" ); document.write( "Solve for \"y\": \n" ); document.write( "y = 57-24 \n" ); document.write( "y = 33 (This is the denominator) \n" ); document.write( "--------------------------------------- \n" ); document.write( "Cheers, \n" ); document.write( "Stan H. \n" ); document.write( "-------------------- \n" ); document.write( " \n" ); document.write( " |