Finding the battery voltages in this circuit

[Eitan Levy]

Homework Statement

This circuit is given:[/B]

What are the values of ε₁ and ε₃?

Homework Equations

IR=V

The Attempt at a Solution

I get the right answer for ε₁ (3V).
But I get that ε₃=12V and not 15 (the answer in the textbook).
First the charge from a to b is 3A.
Then I simply use Kirchhoff's second law, which gives: 2I_ab-6+10+2-ε₃=0.
That gives ε₃=12.
Am I wrong or the book? Maybe the charge from a to b is not 3A?

 

[phinds]

Am I wrong or the book?

book is wrong

Maybe the charge from a to b is not 3A?

How could that POSSIBLY be true? If it were, then the currents into/out of node b would not add up to zero. A miracle.