SOLUTION: what is the formula for find the center of gravity is the wieght are known for both ends and the length of the beam they are attached to how do i find the distance from the ends

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Question 105438: what is the formula for find the center of gravity is the wieght are known for both ends and the length of the beam they are attached to how do i find the distance from the ends to the center of gravity/balance point.

beam is 12ft long the wieghts are a=79 lbs and b=33 lbs what is the distance a= x ft b= x ft
thank you

Found 2 solutions by checkley75, Ahmath:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
79X=33(12-X)
79X=396-33X
79X+33X=396
112X=396
X=396/112
X=3.536 FEET FROM THE BALANCE POINT FOR THE 79 POUND WEIGHT.
12-3.536=8.464 FEET FROM THE BALANCE POINT FOR THE 33 POUND WEIGHT.
PROOF
79*3.536=33*8.464
279.3=279.3

Answer by Ahmath(7) About Me  (Show Source):
You can put this solution on YOUR website!
the wieght times the length divided by the combined wieght79*12 =948 the combined wieght is 79+33= 112, 948/112=8.464ft this is the length of the side with the smallest wieght 33lbs. then 33*12=396 then 396/112= 3.536ft this is the distance for the side with the largest wieght 79lbs. gives you the center of gravity on the 12ft beam. left to right 3.536ft >|< 8.464ft 3.536+8.464= 12ft. the length of the beam.