Step 1 :Let's denote the number of cables A, B, and C produced as \(x\), \(y\), and \(z\) respectively. Then we have the following equations based on the number of wires used:
Step 2 :For black wires: \(3x + y + 2z = 95\)
Step 3 :For white wires: \(3x + 2y + z = 100\)
Step 4 :For red wires: \(2x + y + 2z = 90\)
Step 5 :We can solve this system of equations to find the values of \(x\), \(y\), and \(z\).
Step 6 :The solution to the system of equations is \(x = 5\), \(y = 30\), and \(z = 25\).
Step 7 :Final Answer: The company made \(\boxed{5}\) type A cables, \(\boxed{30}\) type B cables, and \(\boxed{25}\) type C cables.