Answer
$2187$
Work Step by Step
Let $x$ be the number of adult tickets, then $5200-x$ is the number of child tickets, thus our equation will be: $7.5x+4.5\cdot(5200-x)=29961\\7.5x+23400-4.5x=29961\\3x+23400-23400=29961-23400\\3x=6561\\3x/3=6561/3\\x=2187$