SOLUTION: Gabe, a Nuclear Physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 li

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Question 570856: Gabe, a Nuclear Physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid 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
given:
(1) +a+%2B+b+=+90+
(2) +%28+.3a+%2B+.6b+%29+%2F+90+=+.5+
----------
(2) +.3a+%2B+.6b+=+.5%2A90+
(2) +.3a+%2B+.6b+=+45+
(2) +3a+%2B+6b+=+450+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+6b+=+450+
(1) +-3a+-+3b+=+-270+
+3b+=+180+
++b+=+60+
and, since
(1) +a+%2B+b+=+90+
(1) +a+%2B+60+=+90+
(1) +a+=+30+
30 liters of 30% solution are needed
60 liters of 60% solution are needed
check:
(2) +%28+.3a+%2B+.6b+%29+%2F+90+=+.5+
(2) +%28+.3%2A30+%2B+.6%2A60+%29+%2F+90+=+.5+
(2) +%28+9+%2B+36+%29+%2F+90+=+.5+
(2) +45%2F90+=+.5+
(2) +45+=+45+
OK