Question

200 years ago, as it became more and more evident that the

country would sever all ties with England, a large number of people who had
moved here decided to return to their former home. This migration was so
large, in fact, that by July 4, 1776, it had decreased the American population
by 20%, and increased the population of the British Isles by 4%. Assuming
that no one who left America went anywhere else, what percent of the British
popustion was the American population before the migration?

Answer 1

The American population was 20% of the British population.

Explanation:

Let us call
`A` the american population,
`B` the British population before the migration, and
`x` the population that migrated from America to Britannia.

Now, the population
`x` that migrated was 20% of the american population:

`(1).\: \: x = 0.2A`,

and the same population
`x` increase the British population by 4%:

`x+B = 1.04B \\\\ (2). \:\:x = 0.04B.`

Combining equation (1) and (2) we get:

`0.2A = 0.04B`

`A = (0.04B)/(0.2)`

`\boxed{A = 0.2B}`

Thus, the American population was 20% of the British population.