Question 1162410
.
<pre>

In this problem,  "no profit"  means  P = 0.


So, to determine the ticket price,  you need to solve this quadratic equation


    950c - 9.5c^2 = 0.


Factor left side to get


    9.5c*(100 - c) = 0.


It has two roots  c = 0 (which corresponds to distributing the tickets for free)  and  c = 100.
</pre>

Solved.