There are 489 tickets costing $80 and 201 tickets costing $35.
number of $80 ticket = x
number of $35 ticket = 690 - x
sale of $80 ticket = $80x
sale of $35 ticket = $35 (690 - x)
80x + 35(690 - x) = 46155
80x + 24150 - 35x = 46155
80x - 35x = 46155 - 24150
45x = 22005
45x / 45 = 22005 / 45
x = 489 * TICKETS COSTING $80
number of tickets costing $30 = 690 - x = 690 - 489 = 201
To check
$80 x 489 = 39120
$35 x 201 = 7035
39120 + 7035 = 46155