SOLUTION: Dr. Jekyll needs 12 liters of a 40% solution to become Mr. Hyde. He must mix a 20% solution and a 50% solution. How many liters of each will be required to obtain what he needs?

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Question 1104555: Dr. Jekyll needs 12 liters of a 40% solution to become Mr. Hyde.
He must mix a 20% solution and a 50% solution. How many liters of
each will be required to obtain what he needs?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 20% solution needed
Let +b+ = liters of 50% solution needed
-----------------------------------------
(1) +a+%2B+b+=+12+
(2) +%28+.2a+%2B+.5b+%29+%2F+12+=+.4+
-----------------------------------
(2) +.2a+%2B+.5b+=+4.8+
(2) +2a+%2B+5b+=+48+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
------------------------------------
(2) +2a+%2B+5b+=+48+
(1) +-2a+-+2b+=+-24+
------------------------
+3b+=+24+
+b+=+8+
and
(1) +a+%2B+8+=+12+
(1) +a+=+4+
-----------------------------------
4 liters of 20% solution are needed
8 liters of 50% solution are needed
------------------------------------
check:
(2) +%28+.2a+%2B+.5b+%29+%2F+12+=+.4+
(2) +%28+.2%2A4+%2B+.5%2A8+%29+%2F+12+=+.4+
(2) +%28+.8+%2B+4+%29+%2F+12+=+.4+
(2) +4.8+=+.4%2A12+
(2) +4.8+=+4.8+
OK