Question

A patient weighs 139lb. and the order is for 0.15mg of drug per kilogram of body weight. If the drug label indicates the concentration to be 3mg/mL, how many millilitres should you administer? Use 1 kg = 2.2 lbs and round your final answer to 2 decimal places if necessary.

Answer 1

3.16 mL

Explanation:

The patient weighs 130 lb.

Since the order is for 0.15mg of drug per kilogram of body weight, convert the weight of the patient to kg.

`\begin{gathered} 2.2\;lbs=1\text{ kg} \\ 1\;lbs=(1)/(2.2)\text{ kg} \\ \implies139\text{ lb}=139*(1)/(2.2)=63.1818\text{ kg} \end{gathered}`

Next, determine the total mg of drug the patient requires.

`\begin{gathered} \text{0.15mg of drug per kilogram of body weight.} \\ \text{Total mg of drug needed}=0.15*63.1818=9.4772\;mg \end{gathered}`

The drug label indicates the concentration to be 3mg/mL:

`\begin{gathered} 9.4772\;mg/(3mg)/(mL) \\ =(9.4772\;mg* mL)/(3\;mg) \\ =3.16\text{ mL} \end{gathered}`

You should administer 3.16 mL of the drug (correct to 2 decimal places).