A nurse has two solutions that contain different concentrations of a certain medication. One is a 30% concentration and the other is a 15% concentration. How many cubic centimeters of each should she mix to obtain 45 cc of a 20% solution?

Feb 14, 2016

30% medication: 15cc
15% medication: 30cc

Explanation:

Let $x$ be the amount of 30% concentration medication needed
$\implies 45 - x$ is the amount of 15% concentration medication needed

$0.30 x + 0.15 \left(45 - x\right) = 0.20 \left(45\right)$

$\implies 30 x + 15 \left(45 - x\right) = 20 \left(45\right)$

$\implies 30 x + 675 - 15 x = 900$

$\implies 15 x = 225$

$\implies x = 15$

$45 - x = 30$