SOLUTION: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 30 L of a 45% disinfectant solution?

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Question 798711: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 30 L of a 45% disinfectant solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 75% solution needed
Let +b+ = liters of 25% solution needed
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(1) +a+%2B+b+=+30+
(2) +%28+.75a+%2B+.25b+%29+%2F+30+=+.45+
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(2) +.75a+%2B+.25b+=+.45%2A30+
(2) +.75a+%2B+.25b+=+13.5+
(2) +75a+%2B+25b+=+1350+
Multiply both sides of (1) by +25+ and
subtract (1) from (2)
(2) +75a+%2B+25b+=+1350+
(1) +-25a+-+25b+=+-750+
+50a+=+600+
+a+=+12+
and, since
(1) +a+%2B+b+=+30+
(1) +b+=+18+
12 liters of 75% solution are needed
18 liters of 25% solution are needed
check:
(2) +%28+.75a+%2B+.25b+%29+%2F+30+=+.45+
(2) +%28+.75%2A12+%2B+.25%2A18+%29+%2F+30+=+.45+
(2) +%28+9+%2B+4.5+%29+%2F+30+=+.45+
(2) +13.5+=+.45%2A30+
(2) +13.5+=+13.5+