An input force of 50 newtons is applied through a distance of 10 meters to machine with mechanical advantage of 3. if the work output for the machine is 450 newton x meters and this work is applied through a distnace of 3 meters, what is the output force of the machine

The output of the machine is

                                      (output work) =  (output force) x (distance)

                                        450 N-m      =  (output force) x (3 meters)

Divide each side
by  3 meters:                Output force = (450 N-m) / (3 m)

                                                           =    150 newtons .

With all the information given about the output work, we don't need
to know anything about the input work, or even the fact that we're
dealing with a machine.

It's comforting, though, to look back and notice that the output work
(450 N-m) is not more than the input work (500 N-m).  So everything
is nice and hunky-dory.


Well, my goodness !
I didn't even need to go through all of that.

Given:

-- The input force to the machine is 50 newtons.

-- The mechanical advantage of the machine is 3 .

That right there tells us that

-- The output force of the machine is 150 newtons.

We don't need any of the other given information.