Question

a certain antihistamine is often prescribed for allergies. a typical dose for a 100 - pound person is 21 mg every six hours. complete parts (a) and (b) below. a. following this dosage, how many 13.2 mg chewable tablets would be taken in a week? b. this antihistamine also comes in a liquid form with a concentration of 13.2 mg/6 ml. following the prescribed dosage, how much liquid antihistamine should a 100 - pound person take in a week? a. a 100 - pound person could take tablets in a week. (round to the nearest whole number as needed.)

Explanation:

Step1: Calculate the number of 6 - hour intervals in a week

There are 24 hours in a day and 7 days in a week. So the total number of hours in a week is $24\times7 = 168$ hours. The number of 6 - hour intervals in a week is $\frac{168}{6}=28$ intervals.

Step2: Calculate the total amount of antihistamine taken in a week

A 100 - pound person takes 21 mg every 6 hours. So the total amount of antihistamine taken in a week is $21\times28 = 588$ mg.

Step3: Calculate the number of 13.2 - mg tablets

To find the number of 13.2 - mg tablets, divide the total amount of antihistamine taken in a week by the amount of antihistamine per tablet. Let $n$ be the number of tablets. Then $n=\frac{588}{13.2}\approx44.545$. Rounding to the nearest whole number, $n = 45$.

Step4: Calculate the volume of liquid antihistamine

The liquid antihistamine has a concentration of 13.2 mg/6 mL. Let $V$ be the volume of the liquid antihistamine. We know that the total amount of antihistamine is 588 mg. Using the proportion $\frac{13.2}{6}=\frac{588}{V}$, we can cross - multiply to get $13.2V=588\times6$. Then $V=\frac{588\times6}{13.2}=\frac{3528}{13.2}\approx267.27$ mL.

Answer:

a. 45
b. 267.27 mL