Question

A small country is made up of two islands: a big island and a small island. There are currently 530,000 people living on the two islands. Each year, 3% of the people on the big island move to the small one, and 7% of the people on the small island move to the big one. Assuming the population of the country remains at 530,000, how many people will eventually live on the big island?

Answer 1

371,000

Explanation:

The population will stabilize at a level that has the same number moving in each direction each year. If "b" and "s" represent the numbers of people on the "big" and "small" islands, respectively, we want ...

b + s = 530,000

.03b = .07s

From the second equation, ...

s = (3/7)b . . . . . divide the above equation by .07 and simplify

Substituting this into the first equation, we get ...

b + (3/7)b = 530,000

(10/7)b = 530,000 . . . . collect terms

b = (7/10)(530,000) = 371,000 . . . . . . divide by the coefficient of b

The big island population will stabilize at 371,000 people.