# dma 040

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42 inch board is cut into 3 pieces. Piece 2 is twice as long as the 1st & 3rd piece. Piece 3 is three times as long as piece 1. Find inches of all three pieces

• dma 040 - ?? -

Is piece 2 twice as long as 1 & 3 combined? Or separately?

• dma 040 -

separately

• dma 040 -

If piece 2 is twice piece 1, then
x = piece 1
3x = piece 3 (3 times piece 1)
2x = piece 2 (twice piece 1)
x + 3x + 2x = 42
6x = 42
x = 7
Piece 1 - 7
Piece 2 - 14
Piece 3 - 21

• dma 040 -

If piece 2 is twice piece 3, then
x = piece 1
3x = piece 3 (3 times piece 1)
2(3x) = piece 2 (twice piece 3)
x + 3x + 2(3x) = 42
10x = 42
x = 4.2
Piece 1 - 4.2
Piece 2 - 12.6
Piece 3 - 25.2

• dma 040 -

If piece 2 is twice piece 1 & 3, then
x = piece 1
3x = piece 3 (3 times piece 1)
2(3x + x) = piece 2 (twice piece 1 & 3)
x + 3x + 2(4x) = 42
12x = 42
x = 3.5
Piece 1 - 3.5
Piece 2 - 10.5
Piece 3 - 28

• dma 040 -

I'm confused. Shouldn't pc 2 be the largest since it says that pc2 is twice as long as pc 1&3, and pc 3/three times as long as pc1