# Question 708f5

Jan 17, 2017

Here's what I got.

#### Explanation:

You know that you are starting with a 0.4% solution, presumably a mass by volume percent concentration, that you dilute by a factor of $10$.

Before the dilution, the initial solution contained $\text{0.4 g}$ of solute, which is your drug, for every ${\text{100 cm}}^{3}$ of solution.

When you dilute this solution by a factor of $10$, you ensure that the same amount of solution, let's say ${\text{100 cm}}^{3}$, contains $10$ times less solute than the original solution. In other words, the starting solution must be $10$ times more concentrated than the diluted solution.

This means that after the dilution, the solution will contain

$\text{0.4 g"/10 = "0.04 g}$

of drug for every ${\text{100 cm}}^{3}$ of solution. To make the calculations easier, convert this to milligrams of drug

0.04 color(red)(cancel(color(black)("g"))) * (10^3"mg")/(1color(red)(cancel(color(black)("g")))) = "40 mg"

Therefore, you can say that for the diluted solution, you have

"40 mg drug " -> " 100 cm"^3 color(white)(.)"solution" " "color(orange)("(*)")#

Now, the patient received $\text{120 mg}$ of this drug in $3$ doses, meaning that you have

$\text{120 mg drug"/"3 doses" = "40 mg drug / dose}$

You can thus say that the patient received $\text{40 mg}$ of drug per dose and that each dose had a volume of ${\text{100 cm}}^{3}$, as shown by relation $\textcolor{\mathmr{and} a n \ge}{\text{(*)}}$.