SOLUTION: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 25L of a 35% disinfectant solution?

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Question 755841: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 25L of a 35% 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
+.75a+ = liters of disinfectant in 75% solution
+.25a+ = liters of disinfectant in 25% solution
-------------------
given:
(1) +a+%2B+b+=+25+
(2) +%28+.75a+%2B+.25b+%29+%2F+25+=+.35+
-----------------------------
(2) +.75a+%2B+.25b+=+.35%2A25+
(2) +.75a+%2B+.25b+=+8.75+
(2) +75a+%2B+25b+=+875+
Multiply both sides of (1) by +25+ and
subtract (1) from (2)
(2) +75a+%2B+25b+=+875+
(1) +-25a+-+25b+=+-625+
+50a+=+250+
+a+=+5+
and, since
(1) +a+%2B+b+=+25+
(1) +5+%2B+b+=+25+
(1) +b+=+20+
5 liters of 75% solution are needed
20 liters of 25% solution are needed
check:
(2) +%28+.75a+%2B+.25b+%29+%2F+25+=+.35+
(2) +%28+.75%2A5+%2B+.25%2A20+%29+%2F+25+=+.35+
(2) +%28+3.75+%2B+5+%29+%2F+25+=+.35+
(2) +8.75+=+.35%2A25+
(2) +8.75+=+8.75+
OK