Looks like this list might be helpful:
http://boxofficemojo.com/about/adjuster.htm
It is largely about how to adjust for inflation, but the list to the right looks like actual prices for each year starting in 1910.
This site may also help you generally:
http://www.natoonline.org/statisticstickets.htm
Since these are averages, I suppose some theater might have had a cheap ticket for half off somewhere. So ten cents might have been right in a few cases, maybe. Otherwise, it looks like about 24 cents.
Also, I'm wondering where these are averages, if any ticket would've cost 24 cents. Maybe more like an even 20 or 25? I dunno.
search strategy (Google search): movie ticket costs history