A carpenter sawed a piece of wood into 3 pieces. The ratio of the pieces is 1:3:6. The longest piece is 2.5 feet longer than the shortest piece. Find the length of the original piece
let the three pieces be
x , 3x, and 6x
6x - x = 2.5
5x = 2.5
x = .5
three pieces are .5 , 1.5, and 3 ft
the piece was x+3x+6x or 10 long
so 10x = 10(.5) = 5 ft
mmmhh, what about the wood lost due to the sawdust?
You must have one of those fancy new laser saws.
Let's denote the length of the shortest piece as x feet.
According to the given ratio 1:3:6, the lengths of the three pieces are x feet, 3x feet, and 6x feet, respectively.
We are also told that the longest piece is 2.5 feet longer than the shortest piece, which means that the length of the longest piece is x + 2.5 feet.
Since the original piece was sawed into three pieces, the sum of the lengths of all three pieces must equal the length of the original piece.
Therefore, we can set up the following equation:
x + 3x + 6x = x + x + 2.5
Simplifying this equation, we get:
10x = 2x + 2.5
Subtracting 2x from both sides, we have:
8x = 2.5
Dividing both sides by 8, we find:
x = 0.3125
Hence, the length of the original piece of wood is x = 0.3125 feet, or 31.25 inches.