Question #322475

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.)


1
Expert's answer
2022-04-05T15:17:36-0400

Define:

x lbs - unknown weight

y ft - distance from the fulcrum in the first instance

We can make the following system of equations:

xy=406x\cdot y=40\cdot 6

x(y3)=20712x(y-3)=20\cdot 7\frac12

Let’s solve it. From the second equation:

xy3x=20712=150xy-3x=20\cdot 7\frac12=150

Putting the first equation into the second we will obtain:

4063x=15040\cdot6-3x=150

3x=903x=90

x=30x=30

30y=40630\cdot y=40\cdot6

y=8y=8

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


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