Step 1 :Let's denote the number of cases sold as x and the number of t-shirts sold as y.
Step 2 :From the problem, we know that the total number of items sold is 48, so we can write the equation as \(x + y = 48\).
Step 3 :We also know that the total amount of money made is $350, and since each case sells for $10 and each t-shirt sells for $5, we can write the equation as \(10x + 5y = 350\).
Step 4 :We can solve this system of equations to find the values of x and y.
Step 5 :The solution to the system of equations is x = 22 and y = 26.
Step 6 :This means that 22 cases and 26 t-shirts were sold.
Step 7 :Final Answer: \(\boxed{22 \text{ cases, 26 t-shirts}}\)