SOLUTION: Solution A has 16% acid. Solution B has 9% acid. How many liters of each should be mix together to get 35 liters than its 12% ACID? THANK YOU

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Question 647639: Solution A has 16% acid. Solution B has 9% acid. How many liters of each should be mix together to get 35 liters than its 12% ACID?
THANK YOU

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of solution A
Let +b+ = liters of solution B
+.16a+ = liters of acid in 16% solution
+.09b+ = liters of acid in 9% solution
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(1) +a+%2B+b+=+35+
(2) +%28+.16a+%2B+.09b+%29+%2F+35+=+.12+
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(2) +.16a+%2B+.09b+=+.12%2A35+
(2) +.16a+%2B+.09b+=+4.2+
(2) +16a+%2B+9b+=+420+
Multiply both sides of (1) by +9+
and subtract (1) from (2)
(2) +16a+%2B+9b+=+420+
(1) +-9a+-+9b+=+315+
+7a+=+105+
+a+=+15+
and
(1) +15+%2B+b+=+35+
(1) +b+=+20+
15 liters of solution A are needed
20 liters of solution B are needed
check:
(2) +%28+.16%2A15+%2B+.09%2A20+%29+%2F+35+=+.12+
(2) +%28+2.4+%2B+1.8+%29+%2F+35+=+.12+
(2) +4.2+%2F+35+=+.12+
(2) +4.2+=+.12%2A35+
(2) +4.2+=+4.2+
OK