Let с be the number of children’s tickets and 2 be the number of adult tickets sold.

Set up equations.

3800 tickets were sold, so we can write: \(a+c=3800\)

The total revenue is $30495, so we can write:

\(9a + 6.50c = 30495\)

Solve by substitution. Using (1), we solve for c to obtain (3):

\(c= 3800-a\)

Substitute (3) to (2) and solve for a: \(9a + 6.50(3800 - a) = 30495\)

\(9a + 24700 - 6.50a = 30495\)

\(2.50a = 5795\)

\(a= 2318\)

Solve for c using (3): \(c=3800 - 2318\)

\(c= 1482\)

So, there were 2318 adult tickets and 1482 children’s tickets sold.