SOLUTION: Find the amount of 6 percent acid solution and the amount of a 14 percent acid solutions pat should combine to prepare 50cc of 12 percent solutions

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Question 607400: Find the amount of 6 percent acid solution and the amount of a 14 percent acid solutions pat should combine to prepare 50cc of 12 percent solutions
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cc's of 6% solution
Let +b+ = cc's of 14% solution
+.06a+ = cc's of acid in 6% solution
+.14b+ = cc's of acid in 14% solution
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(1) +a+%2B+b+=+50+
(2) +%28+.06a+%2B+.14b+%29+%2F+50+=+.12+
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(2) +.06a+%2B+.14b+=+.12%2A50+
(2) +.06a+%2B+.14b+=+6+
(2) +6a+%2B+14b+=+600+
Multiply both sides of (1) by +6+
and subtract (1) from (2)
(2) +6a+%2B+14b+=+600+
(1) +-6a+-+6b+=+-300+
+8b+=+300+
+b+=+37.5+
and, since
(1) +a+%2B+b+=+50+
(1) +a+%2B+37.5+=+50+
(1) +a+=+12.5+
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12.5 cc's of 6% solution are needed
37.5 cc's of 14% solution are needed
check:
(2) +%28+.06a+%2B+.14b+%29+%2F+50+=+.12+
(2) +%28+.06%2A12.5+%2B+.14%2A37.5+%29+%2F+50+=+.12+
(2) +%28+.75+%2B+5.25+%29+%2F+50+=+.12+
(2) +6+%2F+50+=+.12+
(2) +6+=+.12%2A50+
(2) +6+=+6+
OK