1 A pharmacist is to prepare 15 milliliters of special eye d

1).

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?

2% Solution -

20% Solution -

Solution

Let a = ml of 20% solution needed
Let b = ml of 2% solution needed
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{1} a+b=15
(2) (0.2a+0.02b)/15=0.05
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0.2a+0.02b=0.05*15
  0.2a+0.02b=0.75

   20a+2b=75

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Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) 20a+2b=75
(1) -2a-2b=-30

18a=45

a=2.5

and, since

{1} a+b=15
b= 15-2.5

b= 12.5

2.5 ml of 20% solution are needed
12.5 ml of 2% solution are needed