Answer to Question #329351 in Linear Algebra for Maz

Question

A weight A pound on one side of a beam balances a weight of 40 pounds placed 6 feet from the fulcrum on the other side. If the unknow weight is moved 3 feet nearer the fulcrum, it balances a weight of 20 pounds place 7 1/2 feet from the fulcrum. Find the unknow weight and its distance from the fulcrum in the first instance. (Neglect the weight of the beam.)

Answer 1

Let L denote the distance in feet of a weight A from the fulcrum in the first instance. Then as 40 pounds placed 6 feet balance it we may write an equation:

A*L = 40*6 or A*L = 240

If the weight is moved 3 feet, its distance to the fulcrum becomes L-3, and the balance equation may be written as

A*(L-3) = 20 *7 1/2 or A*L - 3*L = 150

Subtracting it from the first equation get

3*L = 90 or L = 30 feet

Then from the first equation

A = 240 / 30 = 8 pounds