A movie theater charges $5 for an adult ticket and $2 for a child's ticket. One Saturday, the theater sold 785 tickets for $3280. How many child's tickets and adult's tickets were sold that Saturday?

5x + 2y = 3280

x+y = 785

x = 785 - y

5 * (785 - y) + 2y = 3280

3925 - 5y + 2y = 3280

3925 - 3280 - 3y = 0

645 = 3y

y=645/3=215

x=785-215 = 570

Adults - 570 tickets, childs - 215 tickets.

570*5 + 215*2 = 3280

570 adult and 215 child and 3,280 in total

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Answer: 215 child tickets, 570 adult tickets.