If 40 pounds of food was donated to the food bank in the first week, the second week, which had twice the amount of food donated as the first week, had 2*40 = 80 pounds of food.
The total amount of food donated to the food bank after the second week is 40+80 = <<40+80=120>>120 pounds.
In the third week, she gave to the homeless 70/100*120 = <<70/100*120=84>>84 pounds of food.
The total amount of food remaining in the food bank after she gave out 70% to the homeless is 120-84 = <<120-84=36>>36 pounds of food.
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