document.write( "Question 811334: Divide 24 in three parts such that they are in AP and their product is 440. \n" ); document.write( "
Algebra.Com's Answer #488699 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First part = x\r\n" );
document.write( "Second part = x+d\r\n" );
document.write( "Third part = x+2d\r\n" );
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document.write( "The two equations are\r\n" );
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document.write( "x + (x+d) + (x+2d) = 24\r\n" );
document.write( "      x(x+d)(x+2d) = 440\r\n" );
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document.write( "Simplifying the first equation:\r\n" );
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document.write( "x + (x+d) + (x+2d) = 24\r\n" );
document.write( "x + x + d + x + 2d = 24\r\n" );
document.write( "           3x + 3d = 24\r\n" );
document.write( "             x + d = 8\r\n" );
document.write( "                 d = 8-x\r\n" );
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document.write( "Substituting in the second equation:\r\n" );
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document.write( "      x(x+d)(x+2d) = 440\r\n" );
document.write( "x(x+8-x)[x+2(8-x)] = 440\r\n" );
document.write( "     x(8)[x+16-2x] = 440\r\n" );
document.write( "          8x(16-x) = 440\r\n" );
document.write( "           x(16-x) = 55\r\n" );
document.write( "            16x-x² = 55\r\n" );
document.write( "        -x²+16x-55 = 0\r\n" );
document.write( "         x²-16x+55 = 0\r\n" );
document.write( "       (x-11)(x-5) = 0\r\n" );
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document.write( "x-11 = 0 ;  x-5 = 0\r\n" );
document.write( "   x = 11;   x = 5\r\n" );
document.write( "d = 8-x  ; d = 8-x \r\n" );
document.write( "d = 8-11 ; d = 8-5\r\n" );
document.write( "d = -3   ; d = 3\r\n" );
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document.write( "One solution:\r\n" );
document.write( "First part = x = 11 \r\n" );
document.write( "Second part = x+d = 11+(-3) = 8\r\n" );
document.write( "Third part = x+2d = 11+2(-3) = 11-6 = 5\r\n" );
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document.write( "11, 8, and 5\r\n" );
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document.write( "Other solution:\r\n" );
document.write( "First part = x = 5 \r\n" );
document.write( "Second part = x+d = 5+3 = 8\r\n" );
document.write( "Third part = x+2d = 5+2(3) = 5+6 = 11\r\n" );
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document.write( "5, 8, and 11\r\n" );
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document.write( "So they are the same. \r\n" );
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document.write( "(The two solutions come from whether you chop \r\n" );
document.write( "a 24-inch stick starting from the right end \r\n" );
document.write( "or starting from the left end.)\r\n" );
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document.write( "Edwin
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