Posted by Anonymous on .
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  ?? 
Anonymous,
Is piece 2 twice as long as 1 & 3 combined? Or separately?

dma 040 
Anonymous,
separately

dma 040 
Jalita,
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 
Jalita,
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 
Jalita,
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 
Anonymous,
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