Total apparent magnitude of eclipsing binary system This is a question from the 2016 USAAAO national exam, for which no solutions are given:


  An eclipsing binary system has a magnitude $m_p$ = 14.2 during the
  primary transit and $m_s$ = 13.7 during the secondary transit. Find
  the normal (non-eclipsed) apparent magnitude of the system.


I assumed that, as is usual for eclipsing binary systems, the higher magnitude/primary transit refers to the complete eclipse of a smaller, hotter star (say Star B), and the lower magnitude/secondary transit refers to Star B passing in front of a larger, cooler Star A.

To find the normal, non-eclipsed apparent magnitude of the system, usually we achieve a relation like $F_A = kF_B$, where k is a constant. Then, as we know the apparent magnitude corresponding to $F_A$ alone, we could easily calculate that for $F_A + F_B$. However, this is where I ran into trouble. I set up the following equation to attempt to find a relation between $F_A$ and $F_B$: $$m_p - m_s = -2.5log(\frac{F_A}{F_A(1-(R_B/R_A)^2)+F_B})$$ 

The denominator in the argument of the logarithm, $F_A(1-(R_B/R_A)^2)+F_B$, expresses the flux observed at the secondary transit. But I have no way that I can see to figure out the ratio between radii, and I can't think of any reasonable assumption that would simplify the equation further (such as $R_B &lt;&lt; R_A$). 

Should this problem be attacked from a different angle? Any help would be much appreciated!
Without information about stellar radii, I think it's reasonable to assume
$R_A \approx R_B$.
Then your equation becomes

$$ m_p - m_s = -2.5 \log \frac{F_A}{F_B} $$

and you can compute $k$ and the non-eclipsed total magnitude.