# Math

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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?

• Math -

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~ :)

• Math -

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

• Math -

Why 72 + 2x = 11x ?
Would you be able to list some of the common sentences for forming this type of equations? Thanks!! :)))

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