The population of State X is double that of State Y. If the population concentration (people per square mile) of State X is triple that of State Y, then what is the ratio of the area of State X to the area of State Y?

Let c = the population of State X and d = the population of State Y.
Since the population of State X is double that of State Y, $c = 2d$

Let e = the area of State X and f = the area of State Y.
The population concentration of State X = $\frac{c}{e}$
The population concentration of State Y = $\frac{d}{f}$

Since the population concentration of State X is triple that of State Y,
$\frac{c}{e} = 3 * \frac{d}{f}$

Substitute $c = 2d$:
$\frac{2d}{e} = 3 * \frac{d}{f}$

Cross multiply and simplify:
$2d * f = 3d * e$
$2f = 3e$
$\frac{e}{f} = \frac{2}{3}$