Question 40935: A company makes 3 types of cable. Cable A requires 3 black,3 white, and 2 red wires. Cable B requires 1 black, 2 white, and 1 red wire. Cable C requires 2 black,1 white, and 2 red. They used 100 black, 110 white, and 80 red. how many were made of each?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A company makes 3 types of cable. Cable A requires 3 black,3 white, and 2 red wires. Cable B requires 1 black, 2 white, and 1 red wire. Cable C requires 2 black,1 white, and 2 red. They used 100 black, 110 white, and 80 red. how many were made of each?
CABLE......QTY.....BLACK...........WHITE.................RED.......
A...........X........3X.............3X....................2X.......
B...........Y........Y..............2Y.....................Y
C...........Z........2Z..............Z.....................2Z
----------------------------------------------------------------------
TOTAL....X+Y+Z....3X+Y+2Z=100....3X+2Y+Z=110...........2X+Y+2Z=80
.......................EQN.I.......EQN.II................EQN.III
EQN.I-EQN.II............-Y+Z=-10............IV
EQN.I*2-EQN.III*3........6X+2Y+4Z-6X-3Y-6Z=200-240=-40
-Y-2Z=-40......Y+2Z=40......................V
EQN.IV+EQN.V.....3Z=30....Z=10
Y=40-2*10=20
SUBSTITUTING IN EQN.III....2X+20+2*10=80
2X=80-40=40
X=20
|
|
|
