Step 1 :Let's denote the cost of a shirt as 's' and the cost of a hat as 'h'.
Step 2 :From the problem, we can derive two equations: \(4s + 3h = 118\) (This is from Collin's purchase) and \(4s + h = 74\) (This is from Elizabeth's purchase).
Step 3 :We can solve this system of equations to find the values of 's' and 'h'.
Step 4 :The solution to the system of equations is {h: 22, s: 13}.
Step 5 :Final Answer: Each shirt costs \(\boxed{13}\) dollars and each hat costs \(\boxed{22}\) dollars.