SOLUTION: a pharmacist has 10% and 30% alcohol solutions instock. to prepare 200mL of 25% solution how much should a pharmacist mix?

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Question 742877: a pharmacist has 10% and 30% alcohol solutions instock. to prepare 200mL of 25% solution how much should a pharmacist mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = mL of 10% solution needed
Let +b+ = mL of 30% solution needed
+.1a+ = mL of alcohol in 10% solution
+.3a+ = mL of alcohol in 30% solution
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(1) +%28+.1a+%2B+.3b+%29+%2F+200+=+.25+ mL
(2) +a+%2B+b+=+200+ mL
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(1) +.1a+%2B+.3b+=+50+
(1) +a+%2B+3b+=+500+
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Subtract (2) from (1)
(1) +a+%2B+3b+=+500+
(2) +-a+-+b+=+-200+
+2b+=+300+
+b+=+150+
and, since
(2) +a+%2B+150+=+200+
(2) +a+=+50+
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50 mL of 10% solution is needed
150 mL of 30% solution is needed
check:
(1) +%28+.1%2A50+%2B+.3%2A150+%29+%2F+200+=+.25+
(1) +%28+5+%2B+45+%29+%2F+200+=+.25+
(1) +50+=+.25%2A200+
(1) +50+=+50+
OK