Both $£4.20$ and $£7.70$ are multiples of $70p$, so $£C$ must also be a multiple of $70p$. The only multiple of $70p$ between $£90$ and $£96$ which is a whole number of pounds is $£91$.

$7$ children and $8$ adults cost $7\times £4.20+8\times £7.70=£29.40+£61.60=£91$.

Or

$18$ children and $2$ adults cost $18\times £4.20 + 2\times £7.70 = £75.60 + £15.40 = £91$.

*This problem is taken from the UKMT Mathematical Challenges.*