Question

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?

Answer 1

Answer:

Randall=68 pounds, Seth's=40, Joanna's=52

Step-by-step explanation:

Randall's = 3x-7

Seth's = 2x-10

Joanna's = 2x+2

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

Find X:

1. Form into an equation (add parentheses)
2. (3x-7) + (2x+2) = 3 (2x-10)
3. REmove parentheses on left side
4. 3x-7+2x+2 = 3 (2x-10)
5. Distribute right side
6. = 6x-30
7. 3x-7+2x+2 = 6x-30
8. Combine like terms
9. 5x-5=6x-30
10. subtract 5x from BOTH sides (always subtract, add, multiply, and divide both sides at the same time)
11. -5=x-30
12. Add 30 to BOTH sides
13. 25=x

Find how many pounds of trash each friend picked up:

Randall's:

1. 3x-7
2. plug in x  
3. 3(25)-7
4. Distribute
5. 75-7
6. = 68

Seth's:

1. 2x-10
2. 2(25)-10
3. 50-10
4. = 40

Joanna's:

1. 2x+2
2. 2(25)+2
3. 50+2
4. =52

Double check your answers:

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

68+52=40(3)

120=120

You're good to go!