a = amount of advance tickets sold
s = amount of same-day tickets sold
we know that for that performance 55 were sold in all, thus a + s = 55.
and since we know each a costs 35, then the whole amount sold was 35a, and for all s sold it was then likewise 30a.
the total amount paid for all 55 that day was 1775, thus 35a + 30a = 1775.
[tex] \bf \begin{cases}
a+s=55\implies \boxed{s}=55-a\\
35a+30s=1775\\
-------------\\
35a+30\left( \boxed{55-a} \right)=1775
\end{cases}
\\\\\\
35a+1650-30a=1775\implies 5a=125
\\\\\\
a=\cfrac{125}{5}\implies a=25 [/tex]
how many s were sold? well s = 55 - a.
