Word Problem

[shanieO]

A company makes three products X, Y, and Z. Each product requires processing by three machines A, B, and C. The time required to produce one unit of each product is shown below.
PRODUCT MACHINE A MACHINE B MACHINE C
X 1 2 2
Y 2 8 3
Z 2 1 4
The machines are available for 200, 525 and 350 hours each month. How many units of each product can be manufactured per month if all three machines are utilized to their full capacity?

I have done:
A + 2B + 2C = 200
2A +8B + 3C = 525
2A + B + 4C = 350

I rearranged A = 200-2B-2C

Substituted into 2(200-2B-2C)+8B+3C=525
2(200-2B-2C)+B+4C=350

Simplified is -4B-4C+8B+3C=525-400
-4B-4C+B+4C=350-400

Rearranged is 4B-C=125
-3B =-50

This is where I am stuck.

Can you help me please.
ShanieO

 

[Gene]

Your equations look good but elimination is better than substitution.
A + 2B + 2C = 200
Times 2 =
2A +4B + 4C = 400
2A +8B + 3C = 525
2A + B + 4C = 350
subtracting the first from the other two
0A +4B -C = 125
0A -3B + 0C = -50
B=50/3
Now substitute to find C then A
But that gives a negative C. Are you sure of the problem?