# A pharmacist has a 10% alcohol solution and a 25% alcohol solution. How many milliliters of each solution will she need to mix together in order to have 200 mL of a 20% alcohol solution?

Mar 10, 2018

10% solution $= 66.67 m L$
25% solution $= 133.33 m L$

#### Explanation:

Let us begin by assigning volume values to each of the solutions.

We will make the 10% solution $x$
This will make the 25% solutions $200 - x$
The final 20% solution will be $200 m l$

The equation for combining the solutions becomes

$.10 \left(x\right) + .25 \left(200 - x\right) = .20 \left(200\right)$

$.1 x + 50 - .25 x = 40$

$.1 x \cancel{+ 50} - .25 x \cancel{- 50} = 40 - 50$

$- .15 x = - 10$

$\frac{\cancel{- .15} x}{\cancel{- .15}} = - \frac{10}{-} .15$

$x = 66.67 m L$

$200 - x = 133.33 m L$