Answer:
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
