a = adult tickets
c = child
c + a = 163 tickets total
rewrite as c = 163-a
5.10c + 9.00a = 1088.70
5.10(163-a) + 9.00a = 1088.70
831.30-5.10a + 9.00a = 1088.70
831.30 +3.9a = 1088.70
3.9a = 1088.70-831.30
3.9a = 257.40
a = 257.40 / 3.9 = 66
66 adult tickets were sold