SOLUTION: Dmitri needs 7 liters of a 24% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of t

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Question 621351: Dmitri needs 7 liters of a 24% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 28% solution and the other an unlimited supply of of the 14% solution. How many liters of each solution should Dmitri use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 28% solution needed
Let +b+ = liters of 14% solution needed
+.28a+ = liters of sulfuric acid in 28% solution
+.14b+ = liters of sulfuric acid in 14% solution
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(1) +a+%2B+b+=+7+
(2) +%28+.28a+%2B+.14b+%29+%2F+7+=+.24+
---------------------------
(2) +.28a+%2B+.14b+=+1.68+
(2) +28a+%2B+14b+=+168+
(2) +2a+%2B+b+=+12+
Subtract (1) from (2)
(2) +2a+%2B+b+=+12+
(1) +-a+-+b+=+-7+
+a+=+5+
and, since
(1) +a+%2B+b+=+7+
(1) +5+%2B+b+=+7+
(1) +b+=+2+
5 liters of 28% solution are needed
2 liters of 14% solution are needed
check:
(2) +%28+.28a+%2B+.14b+%29+%2F+7+=+.24+
(2) +%28+.28%2A5+%2B+.14%2A2+%29+%2F+7+=+.24+
(2) +%28+1.4+%2B+.28+%29+%2F+7+=+.24+
(2) +1.68%2F7+=+.24+
(2) +1.68+=+1.68+
OK