Let the number of children be c, and the number of adults be a.
c + a = 170 (total number of tickets)
Then the cost of each is: $5.90/child, $9.60/adult:
5.9c + 9.6a = 1269.40 (total sales)
Solving as 2 simultaneous equations, we first transform the first equation:
a = 170 - c
Substitute into the 2nd equation:
5.9c + 9.6(170 - c) = 1269.40
Solving gives c = 98, and a = 170 - 98 = 72. This means that 72 adult tickets were sold that day.