# Question 410ad

##### 1 Answer
Sep 25, 2017

Here's what I got.

#### Explanation:

You can start by calculating the total number of grams of this drug that the patient needs in $1$ day.

Since you know that the dosage is set at $\text{1.9 g}$ every $\text{6 h}$, you can say that the patient will need

$\text{1.9 g/6 h" = "1.9 g"/(6color(red)(cancel(color(black)("hours")))) * (24color(red)(cancel(color(black)("hours"))))/"1 day" = "7.6 g"/"1 day" = "7.6 g/day}$

Next, use the fact that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 g" = 10^3color(white)(.)"mg}}}}$

to convert the sample to milligrams

7.6 color(red)(cancel(color(black)("g"))) * (10^3color(white)(.)"mg")/(1color(red)(cancel(color(black)("g")))) = 7.6 * 10^3color(white)(.)"mg"

So, you know that your patient needs $7.6 \cdot {10}^{3}$ $\text{mg}$ of this drug per day. To find the number of tablets needed to deliver this sample to the patient, use the fact that $1$ tablet has a mass of $\text{500 mg}$.

7.6 * 10^3 color(red)(cancel(color(black)("mg"))) * "1 tablet"/(500color(red)(cancel(color(black)("g")))) = "15.2 tablets"

Now, if you cannot split a table into $5$ equal parts so that you can give

$15.2 = 15 \frac{1}{5}$

tablets to the patient--which would be consistent with the fact that the answer must have $1$ significant figure--then my guess is that $\text{1.9 g}$ is a typo and that the actual value is $\text{1.0 g}$.

In this case, you have

$\text{1.0 g/6 h = 4 g/day}$

which means that you will need

4 * 10^3 color(red)(cancel(color(black)("mg"))) * "1 tablet"/(500color(red)(cancel(color(black)("mg")))) = "8 tablets"#

Since the values given to you justify a $1$-sig-fig answer, this is most likely what the problem looked like.