When a force of 200 N is acting to the right and a force of 100 N is acting to the left on a cart, the net force acting on the cart can be calculated as follows:
Net force = Force to the right - Force to the left Net force = 200 N - 100 N = 100 N to the right
Since the net force is 100 N to the right, the cart will move to the right.
Therefore, the correct answer is: The cart will move to the right.