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A 40 milliliter
(mL) bottle of prediluted tea tree oil contains a
5% concentration of the active ingredient. If the seller charges
$14.96 for the total amount of active ingredient in the bottle, what is the price per
mL of the active ingredient?

A $40$ milliliter $(\mathrm{mL})$ bottle of prediluted tea tree oil contains a $5 \%$ concentration of the active ingredient. If the seller charges $\$ 14.96$ for the total amount of active ingredient in the bottle, what is the price per $\mathrm{mL}$ of the active ingredient?

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Unit prices with unit conversions

Full solution

Q. A

40

milliliter

(\mathrm{mL})

bottle of prediluted tea tree oil contains a

5 \%

concentration of the active ingredient. If the seller charges

\$ 14.96

for the total amount of active ingredient in the bottle, what is the price per

\mathrm{mL}

of the active ingredient?

Calculate total active ingredient: Calculate the total amount of active ingredient in milliliters. $\newline$ Since the bottle contains a $5\%$ concentration of the active ingredient, we need to find $5\%$ of $40\,\text{mL}$ . $\newline$ $5\%$ of $40\,\text{mL}$ $\newline$ $= \left(\frac{5}{100}\right) \times 40\,\text{mL}$ $\newline$ $= 0.05 \times 40\,\text{mL}$ $\newline$ $= 2\,\text{mL}$
Calculate price per milliliter: Calculate the price per milliliter of the active ingredient. $\newline$ The total price for the active ingredient is $\$14.96$ , and we have found that the total amount of active ingredient is $2$ mL. $\newline$ $\text{Price per mL} = \frac{\text{Total price}}{\text{Total amount of active ingredient}}$ $\newline$ $= \frac{\$14.96}{2\text{ mL}}$ $\newline$ $= \$7.48$ per mL

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