Question 102031: Carlo who weighs 25 kilograms ,sits 4m. to the left of the fulcrum of the seesaw, while Erwin, who weighs 35kg,sits 2m. to the right of the fulcrum. If Jerome must sit halfway between Erwin and the fulcrum in order to balance the seesaw, how much does Jerome weigh?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! In problems such as these the basic thing to understand is that for each weight on one side
of the fulcrum you must find the product of the weight times its distance from the fulcrum and
then find the sum of all these products on that side. You must do the same for the other side
of the fulcrum. If the "seesaw" is balanced, the sum of the products on one side must equal
the sum of the products on the other side.
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For this problem, the only weight on the left side is the weight of Carlo. The product of
Carlo's weight (25 kg) and that weight is 4 meters from the fulcrum. The product of the
weight and the distance from the fulcrum is 25 times 4 = 100 kilogram*meters.
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That takes care of the left side. Now you need to do the same type of operation for the
right side. The problem tells you that on the right side there are going to be two weights ...
the weight of Erwin (35 kg) that is 2 meters from the fulcrum, and the weight of Jerome (call
this unknown weight J) that is 1 meter from the fulcrum. So we have two products for this side.
The first product is for Erwin. It is 35 kilograms times 2 meters which is 70 kilogram*meters.
The second product is for Jerome. Jerome's weight is J kilograms and we multiply it by the
1 meter distance between Jerome and the fulcrum. This product is J times 1 which is just J.
So on the right side the two products are 70 kilogram*meters plus J kilogram*meters.
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Again, since the seesaw is balanced, the sum of the products for the left side must equal
the sum of the products on the right side. Using the numbers found above, the equation
becomes:
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100 = 70 + J
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Solve this equation by getting rid of the 70 on the right side. Do this by subtracting
70 from both sides to get:
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100 - 70 = J
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Do the subtraction on the left side and the result is:
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30 = J
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This tells us that Jerome weighs 30 kilograms.
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Hope this helps you to understand how you do balance problems such as these. The process
of balancing the weights times their distances on one side of the equation with the weights
times their distances on the other side of the fulcrum is fundamental to solving problems
such as these.
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