A piece of rope is cut into three pieces in the ratio 2:7:11. If the longest piece is 72cm longer than the shortest piece, find the length of the original rope.

Ps: how do I do this type of question?
What are the fixed steps?

first represent the unknowns using variables:

let 2x = shortest piece
let 7x = 2nd longest piece
let 11x = longest piece
from the second statement, the longest piece is 72 longer than the shortest:
11x = 72 + 2x
solving for x,
11x - 2x = 72
9x = 72
x = 8
the length of the original rope is the sum of all lengths:
2x + 7x + 11x
20x = 20*8 = 160 cm

hope this helps~ :)

Thanks!!! :) is there any shorter ways? :)))

Why 72 + 2x = 11x ?

Would you be able to list some of the common sentences for forming this type of equations? Thanks!! :)))

To solve this type of question, follow these fixed steps:

1. Set up equations: Let's assume the shortest piece of rope has a length x cm. Then the three pieces would have lengths 2x cm, 7x cm, and 11x cm, respectively. We also know that the longest piece is 72 cm longer than the shortest piece, so we can write the equation 11x = x + 72.

2. Solve the equation: To find the value of x, solve the equation 11x = x + 72. Subtract x from both sides: 11x - x = 72. Simplifying, we get 10x = 72. Divide both sides by 10: x = 7.2.

3. Calculate the length of the original rope: Now that we have the value of x, we can find the length of the original rope. Since the shortest piece of rope has a length of x cm, the original rope must be 11x cm. Substituting x = 7.2 into this equation, we get the length of the original rope: 11 * 7.2 = 79.2 cm.

Therefore, the length of the original rope is 79.2 cm.