The second neighborhood uses 150 * 2 = <<150*2=300>>300 barrels of water.
The third neighborhood uses 300 + 100 = <<300+100=400>>400 barrels of water.
The first, second, and third neighborhoods together use 150 + 300 + 400 = <<150+300+400=850>>850 barrels of water.
Thus, the fourth neighborhood has 1200 - 850 = <<1200-850=350>>350 barrels of water left for it to use.
#### 350