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A carpenter needs three pieces of wood to complete a furniture. The longest piece must be twice the length of the middle-sized piece. The shortest piece must be 2 in. Shorter than the middle-sized piece. If a board 70 in. Long is to be used, then find the length of each piece.

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JeanaShupp

Answer: Shortest piece = 16 in.

Middle piece = 18 in.

Longest pice = 36 in.

Step-by-step explanation:

Let x be the length of the shortest piece.

as per given, length of the middle piece = x+2

Length of the longest piece=2(x+2)

Total length = 70 in.

i.e. [tex]x+(x+2)+2(x+2)=70[/tex]

[tex]2x+2+2x+4=70\\\\4x+6=70\\\\4x=70-6\\\\4x=64\\\\ x=\dfrac{64}{4}\\\\ x=16[/tex]

Shortest piece = 16 in.

Middle piece = 18 in.

Longest pice = 2(18) in.

= 36 in.

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