SOLUTION: A dehydrated patient needs a 2.6% saline IV. Unfortunately, the hospital only has bags of 8% and 2% saline solutions. How many liters of each solutions should be mixed together to

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Question 372765: A dehydrated patient needs a 2.6% saline IV. Unfortunately, the hospital only has bags of 8% and 2% saline solutions. How many liters of each solutions should be mixed together to yield 2 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 8% solution needed
Let b = liters of 2% solution needed
In words:
(liters of saline)/(liters of solution) = 2.6%
(1) %28.08a+%2B+.02b%29%2F2+=+.026
(2) a+%2B+b+=+2
------------------
From (1):
(1) .08a+%2B+.02b+=+.052
(1) 80a+%2B+20b+=+52
Multiply both sides of (2) by 20 and
subtract from (1)
(1) 80a+%2B+20b+=+52
(2) -20a+-+20b+=+-40
60a+=+12
a+=+.2
And, since
a+%2B+b+=+2
b+=+1.8
.2 liters of 8% solution and 1.8 liters of 2% solution are needed
check answer:
(1) %28.08a+%2B+.02b%29%2F2+=+.026
(1) %28.08%2A.2+%2B+.02%2A1.8%29%2F2+=+.026
(1) %28.016+%2B+.036%29%2F2+=+.026
.052%2F2+=+.026
.052+=+.052
OK