SOLUTION: A dehydrated patient needs a 3.24% saline IV. Unfortunately, the hospital only has bags of 1% and 9%saline solution. How many liters of each of these solutions should be mixed toge

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Question 529845: A dehydrated patient needs a 3.24% saline IV. Unfortunately, the hospital only has bags of 1% and 9%saline solution. How many liters of each of these solutions should be mixed together to yield 5 liters of the desired concentration?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of 1% solution needed
Let b = liters of 9% solution needed
given:
(1) +a+%2B+b+=+5+ liters
(2) +%28.01a+%2B+.09b%29+%2F+5+=+.0324+
---------------------------
(2) +%28.01a+%2B+.09b%29+%2F+5+=+.0324+
(2) +%28.01a+%2B+.09b%29++=+.0324%2A5+
(2) +.01a+%2B+.09b+=+.162+
(2) +a+%2B+9b+=+16.2+
Subtract (1) from (2)
(2) +a+%2B+9b+=+16.2+
(1) +-a+-+b+=+-5+
+8b+=+11.2+
+b+=+1.4+
and, since
(1) +a+%2B+b+=+5+
(1) +a+%2B+1.4+=+5+
(1) +a+=+3.6+
3.6 liters of 1% solution are needed
1.4 liters of 9% solution are needed
check:
(2) +%28.01%2A3.6+%2B+.09%2A1.4%29+%2F+5+=+.0324+
(2) +%28+.036+%2B+.126+%29+%2F+5+=+.0324+
(2) +.162+=+5%2A.0324+
(2) +.162+=+.162+
OK