Solve the Problem $\mathrm { C }$ Requires 2 Black, 1 White, and 2 Red

Solve the problem.
-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. $\mathrm { C }$ requires 2 black, 1 white, and 2 red. The company used 100 black, 110 white and 80 red wires. How many of each type of cable were made?

A) $20 \mathrm {~A} ; 93 \mathrm {~B} ; 10 \mathrm { C }$
B) $20 \mathrm {~A} ; 20 \mathrm {~B} ; 83 \mathrm { C }$
C) $10 \mathrm {~A} ; 20 \mathrm {~B} ; 20 \mathrm { C }$
D) $20 \mathrm {~A} ; 20 \mathrm {~B} ; 10 \mathrm { C }$