The number of adult tickets sold is (2/3)*345 = <<2/3*345=230>>230
If adult tickets cost $13.95 each, the theater made 230*$13.95 = $3208.50 from the sale of adult tickets
The price of a child's ticket is (2/3)*$13.95 = $<<2/3*13.95=9.30>>9.30
Since the theater sold 345 tickets and 230 of them were adult tickets, there were 345-230 = <<345-230=115>>115 children's tickets sold.
From the sale of children's tickets, the theater made $9.30*115 = $1069.50
In total, the theater made $3208.50 + $1069.50 = $<<3208.5+1069.5=4278>>4278 from ticket sales. Answer: \boxed{4278}.