Three friends fill bags with trash at a neighborhood cleanup. Randall's bag weighs
3x - 7 pounds, Seth's bag weighs 2x -- 10 pounds, and Joanna's bag weighs
2x + 2 pounds. Together, Randall's and Joanna's bags weigh 3 times as much as
Seth's bag. How many pounds of trash does each friend pick up?

Randall picks up 68 pounds

Seth picks up 40 pounds

Joanna picks up 52 pounds

Step-by-step explanation:

Let us make an equation in x to find it

∵ Randall's bag weighs  3x - 7 pounds

∵ Joanna's bag weighs  2x + 2 pounds

∵ Seth's bag weighs 2x - 10 pounds

∵ Randall's and Joanna's bags weigh 3 times as much as  Seth's bag

- That means add Randall's bag and Joanna's bag and equate

    the sum by 3 times Seth's bag

∵ Randall's bag + Joanna's bag = 3(Seth's bag)

∴ (3x - 7) + (2x + 2) = 3(2x - 10)

- Simplify the two sides

∴ (3x + 2x) + (-7 + 2) = 3(2x) - 3(10)

∴ 5x + (-5) = 6x - 30

∴ 5x - 5 = 6x - 30

- Add 5 to both sides

∴ 5x = 6x - 25

- Subtract 6x from both sides

∴ -x = -25

- Divide both sides by -1

∴ x = 25

Substitute x by 25 in the weight of each bag

∵ Randall's bag weighs = 3(25) - 7 = 75 - 7

∴ Randall's bag weighs = 68 pounds

∵ Seth's bag weighs = 2(25) - 10 = 50 - 10

∴ Seth's bag weighs = 40 pounds

∵ Joanna's bag weighs  = 2(25) + 2 = 50 + 2

∴ Joanna's bag weighs  = 52 pounds

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: