Let x + 4800 = original population of Orangedale.

Now 3100 people move from Troutville to Orangedale.

The new population of Troutville = x - 3100

The new population of Orangedale = x + 4800 + 3100

Now the new population of Orangedale is eleven times the new population of Troutville.

So now we have:

x + 4800 + 3100 = 11(x - 3100)

x + 7900 = 11x - 34100

7900 = 10x - 34100

42000 = 10x

4200 = x

Original population of Troutville was 4200.

Original population of Orangedale was 9000.