Answer:
Children attended = 154
Students attended = 40
Adults attended = 77
Step-by-step 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 = ![2x](https://tex.z-dn.net/?f=2x)
Ticket price for children = ![\$ 2x \times 5](https://tex.z-dn.net/?f=%5C%24%202x%20%5Ctimes%205)
As per question statement, there were half as many adults as there are children,
so number of adult tickets = ![x](https://tex.z-dn.net/?f=x)
Ticket price for adults = ![\$ x \times 12](https://tex.z-dn.net/?f=%5C%24%20x%20%5Ctimes%2012)
Now, number of students =
![(271-x-2x)\\\Rightarrow (271-3x)](https://tex.z-dn.net/?f=%28271-x-2x%29%5C%5C%5CRightarrow%20%28271-3x%29)
Ticket price for students = ![\$ (271-3x) \times 7](https://tex.z-dn.net/?f=%5C%24%20%28271-3x%29%20%5Ctimes%207)
Total ticket sales = $1974
![\Rightarrow 12x+2x\times 5 +(271-3x)\times 7 = 1974\\\Rightarrow 22x-21x +(271 \times 7) = 1974\\\Rightarrow x = 1974 - 1897\\\Rightarrow x = 77](https://tex.z-dn.net/?f=%5CRightarrow%2012x%2B2x%5Ctimes%205%20%2B%28271-3x%29%5Ctimes%207%20%3D%201974%5C%5C%5CRightarrow%2022x-21x%20%2B%28271%20%5Ctimes%207%29%20%3D%201974%5C%5C%5CRightarrow%20x%20%3D%201974%20-%201897%5C%5C%5CRightarrow%20x%20%3D%2077)
So, number of adults attended = 77
number of children attended = 77
2 = 154
number of students attended = 271 - 77 - 154 = 40