Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 of an adult ticket. Identify the first step if solving this problem aritmetically, which would find the cost of one adult and one child ticket.

The first step to solve this problem arithmetically would be to set up a system of equations based on the given information.

Let's assume the cost of one adult ticket is 'A' dollars, and the cost of one child ticket is 'C' dollars.

From the given information, we know that:
Three adult tickets + three child tickets = $75
3A + 3C = 75

We are also given that the cost of each child ticket is $3 less than the cost of an adult ticket.
C = A - 3

So, the first step would be to set up these two equations.