SOLUTION: A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions. How much of each should she use?

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Question 697168: A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions. How much of each should she use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 5% solution needed
Let +b+ = ml of 12% solution needed
given:
(1) +a+%2B+b+=+700+
(2) +%28+.05a+%2B+.12b+%29+%2F+700+=+.06+
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(2) +.05a+%2B+.12b+=+.06%2A700+
(2) +.05a+%2B+.12b+=+42+
(2) +5a+%2B+12b+=+4200+
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5a+%2B+12b+=+4200+
(1) +-5a+-+5b+=+-3500+
+7b+=+700+
+b+=+100+
and, since
(1) +a+%2B+b+=+700+
(1) +a+%2B+100+=+700+
(1) +a+=+600+
600 ml of 5% solution is needed
100 ml of 12% solution is needed
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check answer:
(2) +%28+.05%2A600+%2B+.12%2A100+%29+%2F+700+=+.06+
(2) +%28+30+%2B+12+%29+%2F+700+=+.06+
(2) +42+=+.06%2A700+
(2) +42+=+42+
OK