I am sorry if my question is too simple, but I am a bit of a beginner on tension. So this is the problem:

A system of two objects suspended over a pulley by a flexible cable is sometimes referred to as an Atwood’s machine. Here, let the mass of the counterweight be 1000 kg. Assume the mass of the empty elevator is 850 kg, and its mass when carrying four passengers is 1150 kg. For the latter case calculate (a) the acceleration of the elevator and (b) the tension in the cable.

So they call:
$$m\_E = 1150kg$$
$$m\_C = 1000kg$$

Now what I don't understand from the explanation I was given is that the tension force and acceleration for both objects is the same in this example.

> 
> We leave the motor out of the system for this calculation, and assume the cable’s mass is negligible and the pulley is frictionless and massless, which assures that the “tension” in the cord has the same magnitude on both sides of the pulley.
> 
> 
> 

How can tension force be the same if tension force is **the weight plus the net force**, and if the weight is different for both objects, **then how is the tension and acceleration the same magnitude on both objects?**