Given that the population density of georgia is 170 people per square mile and 10,100,000 people live in georgia, what is the area of the state? (to the nearest hundred mi2)

The answer is 59,411.76 square miles

The population density is 170 people per square mile. In other words, in 1 square mile, there are 170 people. So, the question is in what area there are 10,100,000 people. Make a proportion:
170 people : 1 square mile = 10,100,000 people : x

After crossing the products:
x = 10,100,000 people * 1 square mile : 170 people
x = 59,411.76 square miles