Question

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?

Answer 1

10% solution `= 66.67 mL`
25% solution `= 133.33mL`

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 `200ml`

The equation for combining the solutions becomes

`.10(x) + .25(200-x) = .20(200)`

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

`.1x cancel(+ 50) -.25x cancel(- 50) = 40 -50`

`-.15x = -10`

`(cancel(-.15)x)/(cancel(-.15)) = -10/-.15`

`x = 66.67 mL`

`200-x = 133.33mL`