# Virginia and Campbell had 100 kilograms of a 20% glycol solution. How much of a 40% glycol solution should be added to get a solution that is 35% glycol?

Oct 9, 2015

$33 \frac{1}{3}$ kgm

#### Explanation:

Suppose we need to add $\textcolor{red}{x}$ kgm of color(red)(40%) glycol to the $\textcolor{b l u e}{100}$ kgm of color(blue)(20%) glycol solution

The resulting mass would be $\textcolor{g r e e n}{\left(100 + x\right)}$ kgm (at a concentration of color(green)(25%))

color(blue)(20% xx 100) + color(red)(40% xx x) = color(green)(25% xx (100+x))

$\Rightarrow \textcolor{w h i t e}{\text{XX}} \textcolor{b l u e}{20} + \textcolor{red}{\frac{2}{5} x} = \textcolor{g r e e n}{25 + \frac{1}{4} x}$

$\Rightarrow \textcolor{w h i t e}{\text{XX}} \left(\textcolor{red}{\frac{2}{5}} - \textcolor{g r e e n}{\frac{1}{4}}\right) x = \textcolor{g r e e n}{25} - \textcolor{b l u e}{20}$

$\Rightarrow \textcolor{w h i t e}{\text{XX}} \frac{3}{20} x = 5$

$\Rightarrow \textcolor{w h i t e}{\text{XX}} x = \frac{100}{3} = 33 \frac{1}{3}$