Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $30 . For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1775 . How many tickets of each type were sold?
number of advance ticket sold?
number of same day ticket sold?

Answer 1

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.

$\bf \begin{cases} a+s=55\implies \boxed{s}=55-a\\ 35a+30s=1775\\ -------------\\ 35a+30\left( \boxed{55-a} \right)=1775 \end{cases} \\\\\\ 35a+1650-30a=1775\implies 5a=125 \\\\\\ a=\cfrac{125}{5}\implies a=25$

how many s were sold? well s = 55 - a.