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.)
Define:
x lbs - unknown weight
y ft - distance from the fulcrum in the first instance
We can make the following system of equations:
Let’s solve it. From the second equation:
Putting the first equation into the second we will obtain:
Answer: A weight is 30lbs, a distance is 8ft
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