Cinema Costs

At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. When a group of adults and children went to see a film, the total cost was £$C$, where $C$ is a whole number greater than $90$ and less than $96$.

What is the value of $C$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.