SOLUTION: Gabe​ Amodeo, a nuclear​ physicist, needs 30 liters of a 40​% acid solution.  He currently has a 30% solution and a 60% solution.  How many liters of each does he

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Question 1108141: Gabe​ Amodeo, a nuclear​ physicist, needs 30 liters of a 40​% acid solution.  He currently has a 30% solution and a 60% solution.  How many liters of each does he need to make the needed 30 liters of 40​% acid​ solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 30% sloution needed
Let +b+ = liters of 60% solution needed
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(1) +a+%2B+b+=+30+
(2) +%28+.3a+%2B+.6b+%29+%2F+30+=+.4+
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(2) +.3a+%2B+.6b+=+12+
(2) +3a+%2B+6b+=+120+
(2) +a+%2B+2b+=+40+
Subtract (1) from (2)
(2) +a+%2B+2b+=+40+
(1) +-a+-+b+=+-30+
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+b+=+10+
and
(1) +a+%2B+10+=+30+
(1) +a+=+20+
He needs 20 liters of 30% solution
and 10 liters of 60% solution
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check:
(2) +%28+.3a+%2B+.6b+%29+%2F+30+=+.4+
(2) +%28+.3%2A20+%2B+.6%2A10+%29+%2F+30+=+.4+
(2) +%28+6+%2B+6+%29+%2F+30+=+.4+
(2) +12+=+.4%2A30+
(2) +12+=+12+
OK