How to balance a see saw using moments example problem

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so let's look at this simple moment

problem we have a teeter-totter of two

people sitting on it the big persons a

thousand Newtons and the small person is

five hundred Newtons they're sitting two

meters away from the middle then the

question is how far away does the big

person have to sit well let's draw

Freebody diagram first of all oops

like this free body diagram of the plank

that they're sitting on so first of all

we have our coordinate axes we have x

and y and we're gonna have 500 Newton's

pushing down right here we're gonna have

a thousand Newton's pushing down

somewhere over on the other side and in

the middle we'll have this reaction

force is what we call out pushing up on

it preventing this whole thing from

dropping down to the ground I know just

to make our lives easier let's put on