SOLUTION: Two boys weighing 100 and 150 lbs . respectively use a 15 ft plank for a teeter totter . Where should the fulcrum be placed for balance?

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Question 88803: Two boys weighing 100 and 150 lbs . respectively use a 15 ft plank for a teeter totter . Where should the fulcrum be placed for balance?
Answer by Earlsdon(6294) (Show Source):
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In order for the teeter-totter to balance in this problem, then:
Where:
and are the weights 100 lbs and 150 lbs of the two boys and and are the distances of the two boys from the center (fulcrum) of the teeter-totter. and
From this, you can write:
1)
Now you are also told that the length of the teeter-totter is 15 feet, so you can write:
2) Rewrite this as:
3) Now substitute this into equation 1) and solve for
1a) Simplify and solve for
Add to both sides.
Divide both sides by 250.
...and

So the fulcrum should be placed 6 feet from end holding the 150-lb boy (9 feet from the other) of the teeter-totter to achieve balance with the two boys.