SOLUTION: 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. They used 100

Algebra ->  Equations -> SOLUTION: 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. They used 100      Log On


   

Question 1162698: 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. They used 100 black, 110 white and 90 red wires. How many of each cable were made?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

    3A + 1B + 2C = 100   (1)    (counting black cables)

    3A + 2B + 1C = 110   (2)    (counting white cables) 

    2A + 1B + 2C =  90   (3)    (counting red cables)


To solve the system, subtract equation (3) from equation (1). You will get

     A            = 100 - 90 = 10.  


Substitute  this value  A= 10 into equations (1) and (2).  You will get then


    B + 2C  = 70    (4)

    2B + C  = 80    (5)


or equivalently


    2B + 4C = 140

    2B + C  =  80
-------------------------- subtract

         3C = 140-80 = 60  ------>  C = 20.


Finally, from (4)  B = 70-2C = 70 - 40 = 30.


ANSWER.   A= 10;  B= 30;  C= 20.

Solved.