I, too, was unable to arrive at a unique answer. To double check, I used a purely algebraic method and I made a list of all the things I knew. Breakdown by age:
- # of people: x
- # of adults: a
- # of children: x - a
Breakdown by sex:
- # of females: 4/9x
- # of males: 5/9x
Breakdown by age and sex:
- # of female adults: 1/3a
- # of female children: 4/9x - 1/3a
- # of male adults: 2/3a = 5/9x - 85
- # of male children: 85
The only new piece of information I gained from scouring the problem was \(\frac{2}{3}a = \frac{5}{9}x - 85 \implies x = \frac{6a}{5} + 153\). This, then, means that we can arbitrarily decide there were any number of adults (cleanly divisible by 5 of course, since there can't be fractional audience members) and find the corresponding number of total audience members.