document.write( "Question 1119478: a rod has a weight of 45 pounds attached to one end, a weight of 65 pounds to the other. it balance at a point 8 inches from the middle. how long is it? Assume that the rod itself is weightless. \n" ); document.write( "

Algebra.Com's Answer #735055 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the rod's total length, in inches.\r\n" );
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document.write( "Since it is balanced at the point 8 inches from the middle, 45 pounds arm is   inches, while the 65 pounds arm is   inches.\r\n" );
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document.write( "The equilibrium condition is \r\n" );
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document.write( "     = .\r\n" );
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document.write( "It is the balance equation.\r\n" );
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document.write( "To solve it, simplify it step by step. As a first step, multiply both sides by 2:\r\n" );
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document.write( "    45*(x+16) = 65*(x-16)\r\n" );
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document.write( "    9*(x+16) = 13(x-16)\r\n" );
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document.write( "    9x + 9*16 = 13x - 13*16\r\n" );
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document.write( "    9*16 + 13*16 = 13x - 9x\r\n" );
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document.write( "    22*16 = 4x  ====>  x =  = 88.\r\n" );
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document.write( "Answer.  The rod's total length is 88 inches.\r\n" );
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