Answer: 74 children attended
86 students attended
37 adults attended
Explanation:
Let x represent the number of children that attended.
Let y represent the number of students that attended.
Let z represent the number of adults that attended.
The movie theater has a seating capacity of 197. It means that
x + y + z = 197- - - - - - - - - - - - -1
The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 1416, It means that
5x + 7y + 12z = 1416- - - - - - - - - - 2
There are half as many adults as there are children. It means that
It means that
z = x/2
x = 2z
Substituting x = 2z into equation 1 and equation 2, it becomes
2z + y + z = 197
y + 3z = 197- - - - - - - - - - - - -3
5 × 2z + 7y + 12z = 1416
10z + 7y + 12z = 1416
7y + 22z = 1416- - - - - - - - - - - 4
Multiplying equation 3 by 7 and equation 4 by 1, it becomes
7y + 21z = 1379
7y + 22z = 1416
Subtracting, it becomes
- z = - 37
z = 37
x = 2z = 2 × 37
x = 74
Substituting x = 74 and z = 37 into equation 1, it becomes
74 + y + 37 = 197
y = 197 - 74 - 37
y = 86