Question 1203711
 The theater charges $5.00 for children,
Let there be x children 

 $7.00 for students, 
Let  there be y students

and the $12.00 for adults. 
Number of adults  will be x/2

A movie theater has a seating capacity of 367.
x+x/2+y =367
multip;y by LCD 2
2x+x+2y = 734
3x+2y = 734------------1

the total tickets sales was $2668

5x+7y+12*(x/2)=2668
11x+7y = 2668-------------2

Multiply (!) by 11 and (2) by 3 and subtract

33x+22y=8074
33x +21y = 8004

y = 70

Plug y =70 in (1)

3x+2y = 734
3x+140 = 734
3x = 734-140= 594 
x = 198

x/2 = 99 (Adults)
x = 198 (children)
y= 70 (students)

Check

99*7+198*5+70*7=2668