SOLUTION: Hi, I have a solution/miture question. I can solve the problem just fine once I get it in the right order... but this one I'm having a hard time putting all the info where it belon

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Question 219575: Hi, I have a solution/miture question. I can solve the problem just fine once I get it in the right order... but this one I'm having a hard time putting all the info where it belongs.
Q) A pharmacist has 20L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8%?
If you could just help me get this in the right format I would would be so thankful!! Thanks!!!
Casie R

Found 2 solutions by RAY100, josmiceli:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= amt added in liters
.
.1(20) + .05x = .08(20+x),,,drug amt,,,,,note total volume is x+20
.
.(2) +.05x = 1.6 + .08x
.
.(.4) = .03 x
.
13.33333 = x in liters
.
.
check,,,.1*20 +.05*13.33333= .08*33.33333
.
2+.667 = 2.6667,,,ok
.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = liters of 5% solution to be added
It doesn't say what the drug is mixed with, so I'll
just call it water.
In words:
(liters of drug in final solution)/(liters of drug + water in final solution) = 8%
given:
In 20 liters of 10% solution, there is
.1%2A20+=+2 liters of drug
In x liters of the 5% solution there is
.05x liters of drug
-------------------------
%282+%2B+.05x%29%2F%2820+%2B+x%29+=+.08
2+%2B+.05x+=+.08%2A%2820+%2B+x%29
2+%2B+.05x+=+1.6+%2B+.08x
.03x+=+.4
x+=+13.333
The Pharmacist must add 13.333 liters of the 5% solution
check answer
%282+%2B+.05x%29%2F%2820+%2B+x%29+=+.08
%282+%2B+.05%2A13.333%29%2F%2820+%2B+13.333%29+=+.08
2.666%2F33.333+=+.07998
(error due to rounding -OK)