Question

To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water should a nurse add?

Answer 1

`"24 ounces"`

Explanation:

Here's a more intuitive approach to use here.

You know that your initial solution has a percent concentration, presumably volume by volume, of `25%`. This means that any volume of this solution contains `1` part solute and `3` parts solvent.

The target solution must have a concentration of `10%`, which means that any volume of this solution will contain `1` part of solute and `9` parts solvent.

Your starting solution has a volume of `16` ounces, or `4` parts, each with a volume of `4` ounces.

In order to get to a solution that has a total of `10` parts, you must add `6` parts of solvent to the initial solution. Since we know that

`"1 part " = " 4 ounces"`

it follows that you must add

`6color(red)(cancel(color(black)("parts"))) * "4 ounces"/(1color(red)(cancel(color(black)("part solvent")))) = "24 ounces"`

of distilled water, which is your solvent, to the initial solution.

The target solution will contain `1` part solute and `9` parts distilled water for a total of `10` parts of solution, and hence have a percent concentration of `10%`.