Answer:
Let the number of balcony seats be b
Let the number of gallery tickets be g 
Let the number of main floor tickets be m
b + g + m  = 1020
b = 2g
m = b + 225
The number of balcony tickets = 318
The number of gallery tickets = 159
The number of main floor tickets = 543
Step-by-step explanation:
Let the number of balcony seats be b
Let the number of gallery tickets be g 
Let the number of main floor tickets be m
i) Therefore we can write b + g + m  = 1020
ii) there were twice as many balcony tickets sold as gallery tickets
    therefore b = 2g      
  g = 0.5b
iii) there were 225 more main floor tickets than balcony tickets
    therefore m = b + 225
iv) using equation ii) and equation iii) in equation i) we can write
      b + g  + m = b + 0.5b + b + 225  = 1020      
 2.5b  = 795     
  b = 318
v) g  = 0.5 b  = 0.5 
 318 = 159
vi) m = b + 225 = 318 + 225 = 543