# What mass of a 10 % solution must I add to a 20 % solution to get 500 g of a 17.5 % solution?

Jan 19, 2017

You must add 125 g of the 10 % solution to 375 g of the 20 % solution.

#### Explanation:

Let the mass of the 10 % solution be $x \textcolor{w h i t e}{l} \text{g}$.

Then the mass of the 20 % solution is $\left(500 - x\right) \textcolor{w h i t e}{l} \text{g}$.

We have the relation

$\text{mass of solute in 10 % solution" + "mass of solute in 20 % solution" = "mass of solute in 17.5 % solution}$

x color(red)(cancel(color(black)("g"))) × 10 color(red)(cancel(color(black)(%))) + (500 - x) color(red)(cancel(color(black)("g"))) × 20 color(red)(cancel(color(black)(%))) = 500 color(red)(cancel(color(black)("g"))) × 17.5 color(red)(cancel(color(black)(%)))

10x + 20(500 - x) = 500 × 17.5

$10 x + \text{10 000} - 20 x = 8750$

$10 x = 1250$

$x = \frac{1250}{10} = 125$

You must add 125 g of the 10 % solution to 375 g of the 20 % solution.

Check:

"125 g"× 10 % + "375 g" × 10 % = "500 g" × 17.5 %

$\text{12.5 g + 37.5 g = 50 g}$

$\text{50 g = 50 g}$

It checks!