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   inches, while the 65 pounds arm is   inches.


The equilibrium condition is 


     = .


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 =  = 88.


Answer.  The rod's total length is 88 inches.