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A 260 m wire is cut into three pieces. The second piece is 4 times as long as the first. The third piece is 2 times as long as the second. How long is each​ piece?

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Answer:

Lengths of each piece are as follows:

  • First piece: 20 m
  • Second piece 80 m
  • Third piece 160

Step-by-step explanation:

Let us use variables to represent the length of each piece of the wire that is cut into three.

Let x be the length of the first piece, y the length of the second piece and z the length of the third piece

Total length:
x + y + z = 260 m

Second piece four times as long as first piece:
y = 4x

Third piece twice as long as second piece:
z = 2y = 2(4x) = 8x

Substituting the for y and z in terms of x in the first equation:
x + 4x + 8x = 260

13x = 260

x = 260/13

x = 20 m

Therefore y = 4x = 4 x 20 = 80 m

z = 2y = 2 x 80 = 160 m

Answer:

Lengths of each piece are as follows:

  • First piece: 20 m
  • Second piece 80 m
  • Third piece 160 m

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