Step 1 :Let's denote the average ticket price for concert A as 'a' and for concert B as 'b'.
Step 2 :From the problem, we can form the following two equations: \(5a + 6b = 1261\) and \(3a + 3b = 687\).
Step 3 :We can solve this system of equations to find the values of 'a' and 'b', which represent the average ticket prices for concerts A and B respectively.
Step 4 :Solving the equations, we get 'a' as 113 and 'b' as 116.
Step 5 :Final Answer: The average ticket cost for concert A is \(\boxed{113}\) dollars, and the average ticket cost for concert B is \(\boxed{116}\) dollars.