I chose be because sum of x and y is equal to F. Would appreciate if each choice was analyzed

*Answer credited to @Asafmen*

This uses Newton’s Third Law, which states: **when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction**.

In order to push the box **X**, the force must be great enough to overcome the force **X** exerts on **Y**.

After the force does so, the “rest” of the force is pushing the box, which is why the force experienced by **X** is less than that **Y** experiences.

Since they are in contact, we can treat this as a plastic collision- where the total Kinetic Energy does not remain the same.

**F=ma**

M changes here, F is constant, so acceleration for **Y+X** will be smaller than **Y**- meaning **X** will experience less force.

F is needed to push both objects, but X experiences the force only after Y is moved. Therefore, the force is smaller.

The frictionless surface reduced this effect, but we cannot neglect it.