Question

A doctor prescribes a medication to a 169 lb patient. The medication is prescribed at a dosage of 5 mg/kg. How much medication should the patient be given?1 lb = 453.6 g

Answer 1

Given data

Patient's mass in lb = 169 lb

Dosage = 5 mg/kg

1 lb = 453.6 g

Chemistry -> Measurements -> Mass and weight

When the doctor prescribes a medication at a dosage of 5 mg/kg, the amount of medication the patient is going to ingest depends on their weight. If the patient's weight were 1 kg, for example, he or she would take 5 mg of that medication.

Based on this logic, we first have to convert the patient's weight from pounds to kilograms, knowing 1 kg is the same as 1000 grams.

Let's use the following conversion factor:

$\frac{1lb}{453.6g}$$\begin{gathered} weight\text{ \lparen kg\rparen= }169lb*\frac{453.6g}{1lb}*\frac{1kg}{1000g} \\ \\ weight\text{ \lparen kg\rparen=}76.66kg \end{gathered}$

Since the patient weighs 76.66 kg, the next step multiplying by the dosage, like the following:

$\begin{gathered} Amount\text{ of medication = }76.66kg*\frac{5mg}{1kg} \\ \\ Amount\text{ of medication = }383.3mg \end{gathered}$

Final answer:

The patient should take 383.3 mg of the medication prescribed.