Thread: Population Density

New York has a population of 20,000,000 in a 50,000 sqaure mile area.
Illinois has a population of 12,000,000 in a 80,000 square mile area.

How many people from New York would have to move to have the same population density as Illinois.

Originally Posted by Mr_Green

New York has a population of 20,000,000 in a 50,000 sqaure mile area.
Illinois has a population of 12,000,000 in a 80,000 square mile area.

How many people from New York would have to move to have the same population density as Illinois.

Let P1 be the population of NY that achieves the same population density
Let P2 be the population of Illinois that achieves the same population density

we want,

P1/50000 = P2/80000
=> P1 = (5/8)P2

Now P1 + P2 = 20 000 000 + 12 000 000 = 32 000 000

=> (5/8)P2 + P2 = 32 000 000
=> (13/8)P2 = 32 000 000
=> P2 ~= 19 692 308

=> P1 ~= 12307693

So the amount of people that have to move from NY is: 20 000 000 - 12 307 693 = 7 692 307