Final answer:
A 3-teaspoonful dose of cough medicine, with 1.96 g of antitussive medication per pint, contains approximately 61.4 milligrams of the medication. This calculation is made by converting the pint to milliliters and grams to milligrams, then using the milliliter value per teaspoon to find the milligrams per 3-teaspoonful dose.
Step-by-step explanation:
To solve the problem of converting a pint of cough medicine into milligrams for a 3-teaspoonful dose, we need to understand the conversion factors between volumes and the concentration of the medication.
First, we note that 1 pint is equivalent to 473.176 milliliters (mL) and a pint of the cough medicine contains 1.96 grams (g) of antitussive medication. Knowing that 1 gram is equal to 1,000 milligrams (mg), we can convert the entire pint to milligrams by multiplying 1.96 g by 1,000 mg/g, resulting in 1,960 mg in a pint.
Using the information from LibreTexts™, we know that 1 teaspoon is approximately 4.93 milliliters. So, for a 3-teaspoonful dose, we have 3 teaspoons times 4.93 mL/teaspoon, which equals to 14.79 mL (approximately).
Finally, to find out how many milligrams of medication are in a 14.79 mL dose, we perform a proportion based on the total volume of the pint:
473.176 mL : 1,960 mg = 14.79 mL : x mg
x mg = (14.79 mL * 1,960 mg) / 473.176 mL
x = 61.387 mg (approximately).
Therefore, there would be approximately 61.4 milligrams of the medication in a 3-teaspoonful dose.