.
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.
Solved.