Answer:
Let a = number of adult tickets sold
 c = number of children's tickets sold
28a + 13c = 12,700---->28a + 13c = 12,700
 a + c = 550------->13a + 13c = 7,150
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 15a = 5,550
 a = 370, c = 180
370 adult tickets, 180 children's tickets