SOLUTION: 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

Algebra ->  Linear-equations -> SOLUTION: 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       Log On


   



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.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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%2F2%2B8 inches, while the 65 pounds arm is  x%2F2-8 inches.


The equilibrium condition is 


    45%2A%28x%2F2%2B8%29 = 65%2A%28x%2F2-8%29.


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 = %2822%2A16%29%2F4 = 88.


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

Solved.