Answer: Karen picked 1200 pounds.
Bob picked 600 pounds.
Gina picked 400 pounds.
Explanation:
Let x represent the number of pounds of oranges that Karen picked.
Let y represent the number of pounds of oranges that Bob picked.
Let z represent the number of pounds of oranges that Gina picked.
Karen picked twice as many pounds as Bob. It means that
x = 2y
y = x/2
Karen picked 3 times as many as Gina picked. It means that
x = 3z
z = x/3
The total weight of the oranges they picked was 2,200 pounds. This means that
x + y + z = 2200- - - - - - - - - -1
Substituting y = x/2 and z = x/3 into equation 1, it becomes
x + x/2 + x/3 = 2200
Cross multiplying by 6, it becomes
6x + 3x + 2x = 13200
11x = 13200
x = 13200/11
x = 1200
y = 1200/2 = 600
z = 1200/3 = 400