Potential applied across two points with batteries

[1MileCrash]

Homework Statement

attached

Homework Equations

The Attempt at a Solution

The first two were pretty simple, but I'm having trouble grasping why my guess for #3 was actually correct. Why are we ignoring the parallel battery/resistor combo up top and just adding the voltages of the two batteries in series?

As I understand it, batteries in series do add voltages, so I get that, I just don't understand why that other battery/resistor has no effect.

 

[BruceW]

the change in potential is not path dependent. So you can calculate the change using the upper path, or as you have done, using the (simpler) lower path.

Edit: you can also calculate the change in potential by using a path that goes through E3 then R1, it will still get you the same answer.