# A nurse wants to add water to 30 ounces of a 10% solution of benzalkonium chloride to dilute it to an 8% solution. How much water must she add?

Sep 5, 2016

7.5 oz

#### Explanation:

Using the standard dilution equation:

${c}_{1} \cdot {v}_{1} = {c}_{2} \cdot {v}_{2}$

Where:
${c}_{1}$ = concentration 1 = 10%
${v}_{1}$ = volume 1 = 30 oz
${c}_{2}$ = concentration 2 = 8%
${v}_{2}$ = volume 2 = ???

Rearranging for ${v}_{2}$ we get:

${v}_{2} = \frac{{c}_{1} \cdot {v}_{1}}{c} _ 2$

${v}_{2} = \frac{10 \cdot 30}{8}$

${v}_{2} = \frac{300}{8}$

${v}_{2} = \frac{300}{8}$

${v}_{2} = 37.5$ oz

We already have 30 oz, so just need to add 7.5 oz.

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