A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. $B$ requires 1 black, 2 white, and 1 red. $C$ requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 90 red wires. How many of each type of cable were made?
A. $5 \mathrm{~A} ; 18 \mathrm{~B} ; 25 \mathrm{C}$
B. $30 \mathrm{~A} ; 5 \mathrm{~B} ; 25 \mathrm{C}$
C. $58 \mathrm{~A} ; 30 \mathrm{~B} ; 22 \mathrm{C}$
D. $5 \mathrm{~A} ; 30 \mathrm{~B} ; 25 \mathrm{C}$

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.