SOLUTION: A chemist mixes one solution that is 10% alcohol with a solution that is 15% alcohol to make 100 milliliters of a solution that is 12% alcohol. How many milliliters of liquid was i

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Question 696425: A chemist mixes one solution that is 10% alcohol with a solution that is 15% alcohol to make 100 milliliters of a solution that is 12% alcohol. How many milliliters of liquid was in the first solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 10% solution
Let +b+ = ml of 15% alcohol
given:
(1) +a+%2B+b+=+100+
(2) +%28+.1a+%2B+.15b+%29+%2F+100+=+.12+
-----------------------------
(2) +.1a+%2B+.15b+=+.12%2A100+
(2) +.1a+%2B+.15b+=+12+
(2) +10a+%2B+15b+=+1200+
Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10a+%2B+15b+=+1200+
(1) +-10a+-+10b+=+-1000+
+5b+=+200+
+b+=+40+
and, since
(1) +a+%2B+b+=+100+
(1) +a+=+100+-+b+
(1) +a+=+100+-+40+
(1) +a+=+60+
60 ml of 10% solution is needed
40 ml of 15% alcohol is needed
check:
(2) +%28+.1a+%2B+.15b+%29+%2F+100+=+.12+
(2) +%28+.1%2A60+%2B+.15%2A40+%29+%2F+100+=+.12+
(2) +%28+6+%2B+6+%29+%2F+100+=+.12+
(2) +12+=+.12%2A100+
(2) +12+=+12+
OK