## Related questions with answers

Assume a penicillin dose of $9000$ units per kilogram of body weight, taken every $6$ hours, is prescribed for the treatment of a bacterial infection. For penicillin, $400,000$ units are equal to $250 \mathrm{mg}$. a. Express the dose in milligrams per kilogram ( $\mathrm{mg} / \mathrm{kg})$ of body weight. b. How many milligrams of penicillin would a $20$-kilogram child take in one day?

Solution

Verifieda) To express the **penicillin dose in milligrams per kilograms**, we have to consider that $400,000$ units of penicillin is equal to $250$ mg. Thus, for $9000$ units taken every $6$ hours, we have

$\begin{align*} \frac{9,000\text{ units}}{\text{ kg}}\times\frac{250\text{ mg}}{400,000\text{ units}}&=\frac{9,000\times250\text{ mg}}{400,000\text{ kg}}\\ &=\frac{2,250,000\text{ mg}}{400,000\text{ kg}}\\ &=5.625\text{ mg/kg} \end{align*}$

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