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

x = volume of 10% solution to use in the mixture

y = volume of 25% solution to use

She wants a 200 mL solution, so x + y = 200.

The first solution contributes 0.10x mL of alcohol, while the second contributes 0.25y mL. Together, they make a solution with 0.20(x + y) = 0.20(200) = 40 mL of alcohol.

$\begin{cases}x+y=200\\0.10x+0.25y=50\end{cases}\implies x=\dfrac{200}3,y=\dfrac{400}3$