Answer to Question #322475 in Linear Algebra for Kenth Smith

Question

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

Answer 1

Define:

x lbs - unknown weight

y ft - distance from the fulcrum in the first instance

We can make the following system of equations:

$x\cdot y=40\cdot 6$

$x(y-3)=20\cdot 7\frac12$

Let’s solve it. From the second equation:

$xy-3x=20\cdot 7\frac12=150$

Putting the first equation into the second we will obtain:

$40\cdot6-3x=150$

$3x=90$

$x=30$

$30\cdot y=40\cdot6$

$y=8$

Answer: A weight is 30lbs, a distance is 8ft