A 150 lb person sits on a spring-mounted chair whose spring has a stiffness of 200 lb/in. How far does the chair sink when the person sits down?
To set up this problem I would use Hooke's Law: $F(x)=kx$. I know I am looking for the distance the spring moves - so I'm looking for $x$. Would $150$ be $F(x)$? Why or why not?
Note that your question is more of a physics question.
Yes, $150$ pounds would be $F(x)$ - a weight can be interpreted as a force in the following way: simply put the weight down some scales - the force you'd need to apply on the other end of the scales to keep them in equilibrium is then equivalent to a force of $150$ pounds.
Note that this interpretation of force as a weight is very much dependent on the magnitude of the gravitational field of the Earth. Applying a force of 100 pounds would allow you to lift someone who has a mass of 500 pounds on the Moon. That's one of the reason why SI units are used all over the world.
Since the LHS is now in pounds, the right hand side has to be in pounds too. Fill in $k$ and $x$ appropriately to get pounds as units (after cancelation). Alternately, divide $F$ by $k$ to get a distance in inches (so what is the unit of $k$?).