SOLUTION: a 200 ml 75% hydrochloric acid solution is to be made by mixing a 60% and 80% solution. how much of each solution should be used?

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Question 988394: a 200 ml 75% hydrochloric acid solution is to be made by mixing a 60% and 80% solution. how much of each solution should be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 60% solution needed
Let +b+ = ml of 80% solution needed
+.6a+ = ml of acid in 60% solution
+.8b+ = ml of acid in 80% solution
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(1) +a+%2B+b+=+200+
(2) +%28+.6a+%2B+.8b+%29+%2F+200+=+.75+
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(2) +.6a+%2B+.8b+=+.75%2A200+
(2) +.6a+%2B+.8b+=+150+
(2) +6a+%2B+8b+=+1500+
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Multiply both sides of (1) by +6+
and subtract (1) from (2)
(2) +6a+%2B+8b+=+1500+
(1) +-6a+-+6b+=+-1200+
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+2b+=+300+
+b+=+150+
and
(1) +a+%2B+b+=+200+
(1) +a+%2B+150+=+200+
(1) +a+=+50+
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50 ml of 60% solution and
150 ml of 80% solution are needed
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check:
(2) +%28+.6a+%2B+.8b+%29+%2F+200+=+.75+
(2) +%28+.6%2A50+%2B+.8%2A150+%29+%2F+200+=+.75+
(2) +%28+30+%2B+120+%29+%2F+200+=+.75+
(2) +150+=+.75%2A200+
(2) +150+=+150+
OK