SOLUTION: how much 2% alcohol must be mixed with 18% alcohol to get 4,000 ml of 3% alcohol?

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Question 559528: how much 2% alcohol must be mixed with 18% alcohol to get 4,000 ml of 3% alcohol?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 2% alcohol needed
Let +b+ = ml of 18% alcohol needed
given:
+.03%2A4000+=+120+ = ml of alcohol in 3% solution
(1) +a+%2B+b+=+4000+ ml
(2) +.02a+%2B+.18b+=+120+ ml
--------------------
(2) +2a+%2B+18b+=+12000+
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2a+%2B+18b+=+12000+
(1) +-2a+-+2b+=+-8000+
+16b+=+4000+
+b+=+250+
and
(1) +a+%2B+b+=+4000+
(1) +a+%2B+250+=+4000+
(1) +a+=+4000+-+250+
(1) +a+=+3750+
3,750 ml of 2% alcohol and 250 ml of
18% alcohol are needed
---------
check answer:
(2) +.02a+%2B+.18b+=+120+
(2) +.02%2A3750+%2B+.18%2A250+=+120+
(2) +75+%2B+45+=+120+
(2) +120+=+120+
OK