SOLUTION: Help me please! 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 ne

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Question 770408: Help me please!
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?
Gabe needs __ liters of the 30% solution.
He also needs ___ liters of the 60% solution.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 30% solution needed
Let +b+ = liters of 60% solution needed
+.3a+ = liters of acid in 30% solution
+.6b+ = liters of acid in 60% solution
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(1) +a+%2B+b+=+30+
(2) +%28+.3a+%2B+.6b+%29+%2F+30+=+.4+
--------------------------
(2) +.3a+%2B+.6b+=+.4%2A30+
(2) +.3a+%2B+.6b+=+12+
(2) +3a+%2B+6b+=+120+
--------------------
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+6b+=+120+
(1) +-3a+-+3b+=+-90+
+3b+=+30+
+b+=+10+
and, since
(1) +a+%2B+b+=+30+
(1) +a+=+20+
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Gabe needs 20 liters of the 30% solution.
He also needs 10 liters of the 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%2F30+=+.4+
(2) +12+=+.4%2A30+
(2) +12+=+12+
OK