Question

Karen,Bob,and Gina picked oranges. Karen picked twice as many pounds as Bob and 3 times as many Gina. The total weight of the oranges they picked was 2,200 pounds. How many pounds of oranges did each person pick?

Answer 1

Answer: Karen picked 1200 pounds.

Bob picked 600 pounds.

Gina picked 400 pounds.

Step-by-step 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