A pharmaceutical laboratory formulates a liquid medication by combining Active Ingredient … — ACT

A pharmaceutical laboratory formulates a liquid medication by combining Active Ingredient X, Stabilizer Y, and Purified Water in a ratio of $3 : 4 : 8$ by volume. A technician needs to prepare a batch of this medication that contains exactly $360\text{ mL}$ of Stabilizer Y. How many total milliliters of liquid medication will this batch contain?

A
$675\text{ mL}$
B
$720\text{ mL}$
C
$990\text{ mL}$
$1,350\text{ mL}$ Answer
E
$5,400\text{ mL}$

Answer

1,350\text{ mL}

To find the total batch volume, determine the value of one part in the ratio. The three components (Active Ingredient X, Stabilizer Y, and Purified Water) are mixed in a ratio of

3 : 4 : 8

, giving a total of

3 + 4 + 8 = 15

parts. Stabilizer Y represents

4

of these parts and has a volume of

360\text{ mL}

. Dividing

360

4

gives

90\text{ mL}

per part. Multiplying

90\text{ mL}

by the total

15

parts yields

1,350\text{ mL}

Step-by-Step Solution

Find the total number of parts in the ratio.

Total parts =

3 + 4 + 8 = 15

parts.

The complete mixture is made up of the sum of the ratio components.

Determine the volume represented by a single ratio part.

Value of

1

part =

\frac{360\text{ mL}}{4} = 90\text{ mL}

Stabilizer Y accounts for

4

parts of the total ratio and has a volume of

360\text{ mL}

Calculate the total volume of the batch.

Total volume =

15 \times 90\text{ mL} = 1,350\text{ mL}

Multiply the single-part volume by the total number of parts.

Key Concept

Solving Part-to-Total Proportions with Multiple Components

Estimated Time:1m 15s

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Step-by-Step Solution

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