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A 60​-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.

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dragonflame0921

The first is 6 inches.

THe second is 24 inches.

The third is 30 inches.

fichoh

The length of all three pieces cut from the 60 inch board are 6, 24 and 30 inches respectively.

Total length of board = 60 inches

Let :

  • Length of first piece = x
  • Length of second piece = 4x
  • Length of third piece = 5x

This means that the sum of all three pieces adds up the total length ;

x + 4x + 5x = 60

10x = 60

x = (60 / 10)

x = 6 inches

Therefore,

  • Length of first piece, x = 6 inches
  • Length of second piece, 4x = 4(6) = 24 inches
  • Length of third piece, 5x = 5(6) = 30 inches

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