Question 1119478
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Let x be the rod's total length, in inches.


Since it is balanced at the point 8 inches from the middle, 45 pounds arm is  {{{x/2+8}}} inches, while the 65 pounds arm is  {{{x/2-8}}} inches.


The equilibrium condition is 


    {{{45*(x/2+8)}}} = {{{65*(x/2-8)}}}.


It is the balance equation.


To solve it, simplify it step by step. As a first step, multiply both sides by 2:


    45*(x+16) = 65*(x-16)

    9*(x+16) = 13(x-16)

    9x + 9*16 = 13x - 13*16

    9*16 + 13*16 = 13x - 9x

    22*16 = 4x  ====>  x = {{{(22*16)/4}}} = 88.


<U>Answer</U>.  The rod's total length is 88 inches.
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Solved.