As Charlie comments he has "made both countries richer". Suryasnato Dasgputa answers this:
In general to increase the average in both countries, someone with an income between $£16,000$ and $£20,000$ (but not exactly either) needs to move from Emerald to Flint, for the reasons above.
2) Decreasing the average income in both countries
3) Increasing one whilst decreasing the other
There are four ways of this happening.
1) Charlie earns over $£20,000$, and moves from Emerald to Flint. Then Emerald's average goes down and Flint's goes up.
2) Charlie earns over $£20,000$and moves from Flint to Emerald. Then Flint's average goes down and Emerald's goes up.
3) Charlie earns less than $£16,000$ and moves from Emerald to Flint. Then Emerald's average goes up and Flint's goes down.
4) Charlie earns less than $£16,000$ and moves from Flint to Emerald. Then Flint's average goes up and Emerald's average goes down.
4) Moving from Emerald to Flint, reducing the average in Emerald and doubling the average in Flint
Thomas Hu from A Y Jackson school answered this;
Well done Thomas, but you haven't explained where you got these equations from. However with a little algebra, we can see where these came from.From part $3$ we know that for the average in Emerald to decrease and the average in Flint to increase we need a person with a salary over $£20 000$ to move from Emerald to Flint. To make the average still valid after the move, Emerald must have more than just our citizen who is moving.
5) Other interesting circumstances
To change the average income of one, and not change the other by moving either way, Charlie must have exactly the income amount of either island.
To make one country not have a valid average income, he must be the only citizen of a country. As average is not valid with only one piece of information.
Suryasnato also noted;
Charlie's move would have unexpected results if when he is about to move, a fire hits Flint and all of the below average earners are wiped out. Then, the average income is increased to $£20,000$. So when Charlie moves, he will be a below average earner and make Flint poorer.
True, though we hope a fire wouldn't wipe out half the residents of an island!
Thomas and Surysnato have spotted some interesting changes, can you find any others?