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Question 1081541: A steel company has three blast furnaces of varying sizes. If furnaces A,B, and C are used full time, 800 metric tons of steel produced per day. If A and B are used half time while C at full time, 545 metric tons are produced. If A is not used, B as full time, and C as half-time, 410 metric tons are produced. How many metric tons per day does each furnace produce?
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
Let a = "How many metric tons per day furnace A produces",
b = same for B,
c = same for C.
Then you have these equations:
a + b + c = 800, (1)
a/2 + b/2 + c = 545, (2)
b + c/2 = 410. (3)
Now multiply eq(2) by 2 (both sides), and then subtract eq(1) from it. You will get
a + b + c = 800 (1)
a + b + 2c = 1090 (4)
--------------------subtract eq(1) from eq(4)
c = 1090 - 800 = 290.
Having this, find b from (3).
Having b and c, find a from (1).
For similar problems, see the lesson
- Joint-work problems for 3 participants
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".
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