SOLUTION: Hello I need help with a solution problem. I can not seem to put this thing together. A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patien

Question 30391: Hello
I need help with a solution problem. I can not seem to put this thing together.

A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 2% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock. How much of each type of solution should be used to fill the prescription.

Help with this will be greatly appreciated, I am lost on this one.
Thanks
Terry
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
First off, real my Lesson on this website on how to do this type of question.

Second, just looking at the question, we have some 10% and some 1% that mix to make a 2% solution.

Just by common sense, we will need more of the 1% solution, since the final answer is a 2% solution. Hoepfully that makes sense? We expect a lot more of the 1% solution to be used.

Right...
Let x = amount of 1% solution used.
So, how much of 10% is used? Answer is (15-x) --> ie everything else to make up the final 15ml.

BEFORE: x of 1% AND (15-x) of 10%
--> 0.01x + 0.10(15-x)

AFTER: 15ml of 2%
--> 0.02*15

And being a mixture, the BEFORE has to equal the AFTER:
0.01x + 0.10(15-x) = 0.02*15
0.01x + 1.5 - 0.10x = 0.30
-0.09x = -1.2
x = -1.2/-0.09
x = 13.3333 ml

and so there are 13.3333ml of the 1% solution and 1.6666ml of the 10% solution.

jon.

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