A patient is prescribed 6 mg of cough medication. The label on the prescription says there are 2 mg per 4 mL. How many teaspoons of cough medication does the patient need to take?

Question

Prescription
_________ x mL = ?
Stock

6mg
___________ x 4 mL = 12mL
2mg

1 tsp = 5 mL
12 / 5 =
Answer: ?

Answer 1

To solve the problem, we first need to determine how many milliliters (mL) of cough medication the patient needs to take to get the prescribed dose of 6 mg.

From the prescription information given:

• The cough medication concentration is 2 mg per 4 mL.

To find out how many mL correspond to 6 mg, we can set up a proportion:

\[ \frac{2 \text{ mg}}{4 \text{ mL}} = \frac{6 \text{ mg}}{x \text{ mL}} \]

Cross-multiplying gives us:

\[ 2 \text{ mg} \cdot x \text{ mL} = 6 \text{ mg} \cdot 4 \text{ mL} \]

This simplifies to:

\[ 2x = 24 \]

Dividing both sides by 2:

\[ x = 12 \text{ mL} \]

Now that we know the patient needs to take 12 mL of cough medication, we convert this volume into teaspoons:

Given that 1 teaspoon (tsp) = 5 mL, we can convert mL to teaspoons:

\[ \frac{12 \text{ mL}}{5 \text{ mL/tsp}} = 2.4 \text{ tsp} \]

So, the patient needs to take 2.4 teaspoons of the cough medication.

Answer: 2.4 teaspoons