Cost of CDs :
The accompanying table shows the total cost of purchasing combinations of differently priced CDs. The types of CDs are labeled A, B, and C.
A B C Total Cost
1 1 1 $37
3 2 1 $69
1 1 4 $82
(a) Let x be the cost of a CD of type A, y be the cost of a CD of type B, and z be the cost of a CD of type C. Write a system of three linear equations that represents the data in the table.
(b) Solve the system and interpret your answer.