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?

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Answer 1 · 2015-08-09T16:52:38

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

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 = (3.8 * cancel(100))/cancel(100) = "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 = (3.8 * 100)/95 = color(green)("4 L")# of the 95% solution.

The volume of water would be

#V_"water" = 100 - V_"sol"#

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