# A nurseryman is preparing an insecticide by mixing a 95% solution with water (0% solution). How much solution and how much water are needed to fill a 100 L tank with 3.8% solution?

Aug 9, 2015

You need 4 L of solution and 96 L of water.

#### Explanation:

The key to solving this problem is understanding that all the solute that exists in the 100-L solution comes from the 95% solution.

This means that you can figure out how much solution you need to mix with water by calculating how much solute you get in the final 100-L sample.

"x L solute"/("100 L solution") * 100 = 3.8%

This means that you have

$x = \frac{3.8 \cdot \cancel{100}}{\cancel{100}} = \text{3.8 L}$ of solute in the final solution.

Now use the percent concentration of the 95% solution to figure out how much solution would contain 3.8 L of solute

"3.8 L solute"/("y L soluteion") * 100 = 95%

This means that you need

$y = \frac{3.8 \cdot 100}{95} = \textcolor{g r e e n}{\text{4 L}}$ of the 95% solution.

The volume of water would be

${V}_{\text{water" = 100 - V_"sol}}$

V_"water" = 100 - 4 = color(green)("96 L")