SOLUTION: A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 20% solut

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Question 768567: A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 20% solution and 2% solution in stock. How much of each type of solution should be used to fill the prescription?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 20% solution needed
Let +b+ = ml of 2% solution needed
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{1} +a+%2B+b+=+15+
(2) +%28+.2a+%2B+.02b+%29+%2F+15+=+.05+
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(2) +.2a+%2B+.02b+=+.05%2A15+
(2) +.2a+%2B+.02b+=+.75+
(2) +20a+%2B+2b+=+75+
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Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +20a+%2B+2b+=+75+
(1) +-2a+-+2b+=+-30+
+18a+=+45+
+a+=+2.5+
and, since
{1} +a+%2B+b+=+15+
(1) +b+=+15+-+2.5+
(1) +b+=+12.5+
2.5 ml of 20% solution are needed
12.5 ml of 2% solution are needed
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check:
(2) +%28+.2a+%2B+.02b+%29+%2F+15+=+.05+
(2) +%28+.2%2A2.5+%2B+.02%2A12.5+%29+%2F+15+=+.05+
(2) +%28+.5+%2B+.25+%29+%2F+15+=+.05+
(2) +.75+=+.05%2A15+
(2) +.75+=+.75+
OK