SOLUTION: A pharmacist is to prepare 18 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 3% active ingredient, but the pharmacist only has 9% s

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Question 399532: A pharmacist is to prepare 18 milliliters of special eye drops for a
glaucoma patient. The eye-drop solution must have a 3% active ingredient,
but the pharmacist only has 9% 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!
In words:
(ml of active ingredient)/(ml of total solution) = 3%
Let a = ml of 9% solution to use
Let b = ml of 2% solution to use
-----------------
given:
.09a = ml of active ingredient in 9% solution
.02b = ml of active ingredient in 2% solution
(1) a+%2B+b+=+18 ml
--------------------
(2) %28.09a+%2B+.02b%29%2F+18+=+.03
(2) .09a+%2B+.02b+=+.54
(2) 9a+%2B+2b+=+54
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) 9a+%2B+2b+=+54
(1) -2a+-+2b+=+-36
7a+=+18
a+=+18%2F7 ml
and, from (1)
(1) a+%2B+b+=+18
b+=+18+-+18%2F7
b+=+%28126+-+18%29%2F7
b+=+108%2F7 ml
18/7 ml of 9% solution must be used
108/7 ml of 2% solution must be used
-------------------------------------
check answer:
(2) %28.09a+%2B+.02b%29%2F+18+=+.03
(2) %28.09%2A%2818%2F7%29+%2B+.02%2A%28108%2F7%29%29%2F+18+=+.03
(2) %289%2A%2818%2F700%29+%2B+2%2A%28108%2F700%29%29%2F+18+=+3%2F100
(2) %289%2A%2818%2F700%29+%2B+2%2A%28108%2F700%29%29%2F+18+=+21%2F700
(2) 162+%2B+216+=+18%2A21
(2) 378+=+378
OK