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?

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

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system