A 61 in. wood plank is cut into 3 pieces. The longest piece is 5 times the length of the smallest piece. The medium piece
less than 2 times the length of the smallest.
1. If z represents the length of the smallest piece, write the expression that represents the medium size piece.
2. Write an equation to show that length of all the pieces together equal to the total length of 61 inches.
3. What is the length of each piece of wood? Explain how you know you are correct.

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Vintechnologygo Vintechnologygo · Answer 1

The length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.

The wood is 61 inches and it is divide into 3 pieces.

The longest piece is 5 times the length of the smallest piece.

The medium piece less than 2 times the length of the smallest.

let

z = length of the smallest piece of wood

longest piece = 5z

medium piece = 2z

The equation to represent the total piece together is equal to 61 inches.

z + 5z + 2z = 61

Therefore, the length of each wood piece can be calculated as follows:

z + 5z + 2z = 61

8z = 61

z = 61 / 8

z = 7.625 inches

longest piece = 5(7.625) = 38.125 inches

medium piece = 2(7.625) = 15.25 inches

Therefore, the length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.

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