Let A = Asians population,
Let B = North American population,
Let C = area of Asia, presumably in square miles,
Let D = area of North America, also in square miles.
I don't know if these land areas are even close to correct, and I don't plan to look it up as it will not matter to the method of solution. And I also do not know where "(land area=1,000mi squared)" is supposed to fit in this particular problem.
The population density is found by (population/area), so for Asia that is A/C, and for North America that is B/D.
( (B/D) / (A/C) ) should give you a percentage comparison, i.e., that the population density of North America is some percentage of the population density of Asia.
I hope this helps.