# A pharmacist has one solution that is 40% iodine and 60% water, and another solution that is 3% iodine. How many liters of each solution should the pharmacist use to make 11 liters of a solution that is 19% iodine?

Aug 28, 2017

The volume of 40% iodine solution is $= 4.76 L$ and the volume of the 3% iodine solution is $= 6.243 L$

#### Explanation:

Let the volume of the solution 40% iodine be $= x L$

Then, the volume of the solution 3% iodine be $= \left(11 - x\right) L$

The material balance with respect to iodine is

$x \cdot 0.4 + \left(11 - x\right) \cdot 0.03 = 11 \cdot 0.19$

$0.4 x + 0.33 - 0.03 x = 2.09$

$0.37 x = 2.09 - 0.33 = 1.76$

$x = \frac{1.76}{0.37} = 4.757 L$