Let x = original population of Troutville.
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.
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