SOLUTION: A 50%sulfuric acid solution is to be mixed with a 75% sulfuric acid solution to get 60 liters of a 60% sulfuric acid solution . How many liters of the 50% solution and the 75% solu

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Question 1091191: A 50%sulfuric acid solution is to be mixed with a 75% sulfuric acid solution to get 60 liters of a 60% sulfuric acid solution . How many liters of the 50% solution and the 75% solution should be mixed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 50% solution needed
Let +b+ = liters of 75% solution needed
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(1) +a+%2B+b+=+60+
(2) +%28+.5a+%2B+.75b+%29+%2F+60+=+.6+
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+.5a+%2B+.75b+=+36+%7D%5D%5D%0D%0A%7B%7B%7B+50a+%2B+75b+=+3600+
(2) +2a+%2B+3b+=+144+
Multiply both sides of (1) by 2 and
subtract (1) from (2)
(2) +2a+%2B+3b+=+144+
(1) +-2a+-2b+=+-120+
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+b+=+24+
and
(1) +a+%2B+24+=+60+
(1) +a+=+36+
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36 liters of 50% solution are needed
24 liters of 75% solution are needed
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check:
+.5a+%2B+.75b+=+36+
+.5%2A36+%2B+.75%2A24+=+36+
+18+%2B+18+=+36+
+36+=+36+
OK