The given information is:
- Cost of each child ticket: $5.10
- Cost of each adult ticket: $9.80
- They sold 3 times as many adult tickets as child tickets
- The total sales were $1311.00
So, we can express this situation in the form of algebraic equations:
Let's set "A" as the number of adult tickets sold, and "C" as the number of child tickets sold, so:

Now, the total sales are given by:

Replace equation 1 into equation 2 and solve for C:

Now, replace C-value into equation 1 and solve for A:

Then, there were sold 38 child tickets and 114 adult tickets.