a certain antihistamine is often prescribed for allergies. a typical dose for a 100-pound person is 20 mg every six hours. complete parts (a) and (b) below.

a. following this dosage, how many 12.3 mg chewable tablets would be taken in a week?
b. this antihistamine also comes in a liquid form with a concentration of 12.3 mg/5 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.)

Question

a certain antihistamine is often prescribed for allergies. a typical dose for a 100-pound person is 20 mg every six hours. complete parts (a) and (b) below.

a. following this dosage, how many 12.3 mg chewable tablets would be taken in a week?
b. this antihistamine also comes in a liquid form with a concentration of 12.3 mg/5 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.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Dimensional Analysis", "Unit Conversion" ], "new_concepts": [ "Dosage Calculation", "Concentration Conversion" ], "current_concepts": [ "Dimensional Analysis", "Unit Conversion", "Dosage Calculation", "Concentration Conversion" ] } ## Calculate total weekly dosage Using the *Dimensional Analysis* and *Unit Conversion* knowledge points $$ \begin{aligned} &\text{Dose} = 20\text{ mg} / 6\text{ hours} \ &\text{Hours per week} = 7\text{ days} \times 24\text{ hours/day} = 168\text{ hours} \ &\text{Total weekly dosage} = 20\text{ mg} \times \frac{168\text{ hours}}{6\text{ hours}} = 560\text{ mg} \end{aligned} $$ ## Determine weekly tablet count Using the *Dimensional Analysis* and *Unit Conversion* knowledge points $$ \begin{aligned} &\text{Tablet strength} = 12.3\text{ mg/tablet} \ &\text{Tablets per week} = \frac{560\text{ mg}}{12.3\text{ mg/tablet}} \approx 45.528\text{ tablets} \ &\text{Rounded to nearest whole number} = 46\text{ tablets} \end{aligned} $$ ## Determine weekly liquid volume Using the *Dimensional Analysis* and *Unit Conversion* knowledge points $$ \begin{aligned} &\text{Liquid concentration} = \frac{12.3\text{ mg}}{5\text{ mL}} \ &\text{Liquid volume per week} = 560\text{ mg} \times \frac{5\text{ mL}}{12.3\text{ mg}} \approx 227.64\text{ mL} \ &\text{Rounded to nearest tenth as needed} = 227.6\text{ mL} \end{aligned} $$ ## Question a A 100-pound person could take 46 tablets in a week. ## Question b Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week? 227.6 mL { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Dimensional Analysis" ] }

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Explanation:

Calculate total weekly dosage

Determine weekly tablet count

Determine weekly liquid volume

Answer:

Question a

Question b