SOLUTION: A chemist needs 6 liters of a 10​% alcohol solution but has only a 15​% alcohol solution. How many liters each of the 15​% solution and water should he mix

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Question 1040218: A chemist needs 6 liters of a 10​%
alcohol solution but has only a
15​% alcohol solution. How many liters each of the
15​% solution and water should he mix to make the desired
6 liters of 10​%
​solution?
The chemist needs to mix
___ liters of
15​% alcohol solution with
___ liters of water.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 15% solution needed
Let +b+ = liters of water needed
-------------------------------
(1) +a+%2B+b+=+6+
(2) ++.15a+%2F+%28+a+%2B+b+%29+=+.1+
---------------------------
By substitution:
(2) +.15a+%2F+6+=+.1+
(2) +.15a+=+.6+
(2) +a+=+4+
and
(1) +a+%2B+b+=+6+
(1) +4+%2B+b+=+6+
(1) +b+=+2+
----------------
4 liters of 15% solution are needed
2 liters of water are needed
-------------------------
check:
(2) ++.15a+%2F+%28+a+%2B+b+%29+=+.1+
(2) ++.15%2A4+%2F+6+=+.1+
(2) +.6+=+.6+
OK