Linear Systems & Matrices · Superchallenge problem

Two towns, A and B, together have $1000$ residents, and nobody enters or leaves the pair of towns. Each year $20\%$ of A's residents move to B and $30\%$ of B's residents move to A, all at once. At the start, all $1000$ live in A. Treating the populations as exact numbers (not rounded), after how many years does the population of A first drop below $601$?