Solving for a force eliminating acceleration

[cwbullivant]

Homework Statement

A worker applies a force of 210N to a box attached to a cart, with sufficient frictional force such that the box and the cart move as one. What is the frictional force on the box?

Force 1: Force on box by worker, F_BW
Force 2: Force on cart by box, F_CB
Force 3: Force on box by cart, F_BC

Homework Equations

The Attempt at a Solution

This is from the solution, but I can't understand how it was obtained, as it doesn't explain the process:

F_CB = M_cartA (I knew this part)
F_BW - F_BC = M_boxA

"Since we want to solve for the unknown F_CB = F_BC, we eliminate A from these two equations and obtain:"

F_CB = (M_cart*F_BW)/(M_cart+M_box)

I don't quite understand what they mean by "eliminate A" (hold it constant?), nor can I seem to deduce the process they used here.

I've tried substituting in M_cartA for F_BC (since they're equal), but all that does is solve for A, which I'm evidently supposed to eliminate to begin with.

 

[Simon Bridge]

This is from the solution, but I can't understand how it was obtained, as it doesn't explain the process:

They have started by drawing free-body diagrams for the box and the cart, then, for each diagram, summed the forces and used Newton's law.
This gives two simultanious equations and two unknowns ... how would you solve them?

I don't quite understand what they mean by "eliminate A"

Then mean that you solve for A in one equation and substitute it into the other one.

 

[cwbullivant]

They have started by drawing free-body diagrams for the box and the cart, then, for each diagram, summed the forces and used Newton's law.
This gives two simultanious equations and two unknowns ... how would you solve them?

Then mean that you solve for A in one equation and substitute it into the other one.

The first became immediately obvious when I read the second. I feel really, -really- dumb right now; I really have no excuse for not getting that. Thanks for the help, much appreciated.

 

[Simon Bridge]

We all do that from time to time - sometimes a change in wording can make the mind go blank.