Answer:
Children attended = 154
Students attended = 40
Adults attended = 77
Explanation:
Seating capacity = 271
Charges for each children ticket = $5
Charges for each student ticket = $7
Charges for each adult ticket = $12
Let number of children tickets =

Ticket price for children =

As per question statement, there were half as many adults as there are children,
so number of adult tickets =

Ticket price for adults =

Now, number of students =

Ticket price for students =

Total ticket sales = $1974

So, number of adults attended = 77
number of children attended = 77
2 = 154
number of students attended = 271 - 77 - 154 = 40