Moment of a Couple, making sure answer is reasonable

[torchflame]

Homework Statement

Given the following structure, determine the value of F such that the resultant couple moment on the structure is 200 pound-feet clockwise.

I'm not looking for help here per se, just if this is a valid method of solution:
Because the moment of a couple is a free vector, it seems to me that the moments of the two couples can be placed at point B without any problem.
Then it would also make sense to me that: $M_{\text{couple with F}}=F\cdot 2\sqrt{2}$ pound-feet clockwise, and $M_{\text{150 lb couple}}=600\sqrt{2}$ pound-feet counterclockwise, which gives me that $F\cdot 2\sqrt{2}-600\sqrt{2}=-200$, which implies that $F=229 \text{ lb}$.
Is this a valid method of solution? It makes sense to me, but I'm not sure if it makes sense to anyone else.

 

[CWatters]

I'm very rusty on this but seems to me that you would need to know force at A to use your method. Perhaps I'm wrong.

 

[pongo38]

look again at your root 2. It's not quite right. You can check your answer by taking moments about any point.