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

Jun 15, 2016

$\text{24 ounces}$

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

$\text{1 part " = " 4 ounces}$

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%.