A carpenter sawed a piece of wood into 3 pieces of wood into 3 pieces. The ratio of wood pieces is 1:3:6. The longest piece is 2.5 feet longer than the shortest piece. Use the draw a diagram strategy to find the length of the original piece.
6x = x + 2.5
x = 0.5
now use that to get the lengths.
or she
To solve this problem using the "draw a diagram" strategy, we can start by visualizing the situation. Let's represent the lengths of the three pieces of wood with variables:
Let's call the length of the shortest piece "x."
According to the problem, the longest piece is 2.5 feet longer than the shortest piece. So we can represent the length of the longest piece as "x + 2.5."
The ratio of wood pieces is given as 1:3:6. This means that the lengths of the three pieces are in the ratio 1:3:6.
To draw a diagram, we can use a line segmented into three parts corresponding to the three pieces of wood. We'll label the lengths of the pieces using the variables we defined.
Now, if we let the shortest piece be x, we can represent the other two pieces as 3x and 6x, respectively. Since the longest piece is 2.5 feet longer than the shortest piece, we can represent it as (x + 2.5).
So our diagram looks like this:
x 3x 6x
|---------------|------------------|-------------------|
Now, based on the information given, we know that these three parts sum up to form the original length of the wood. So we can set up an equation:
x + 3x + 6x = Original Length
Simplifying the equation, we have:
10x = Original Length
To find the length of the original piece, we need to determine the value of x.
Since the longest piece is 2.5 feet longer than the shortest piece, we can set up another equation:
(x + 2.5) = length of the longest piece
Now, using the given ratio, we can equate this length to 6x:
(x + 2.5) = 6x
Simplifying the equation, we have:
2.5 = 5x
Dividing both sides by 5, we get:
0.5 = x
So the shortest piece is 0.5 feet long.
Now that we know the value of x, we can calculate the length of the original piece by substituting it back into our original equation:
10x = Original Length
10(0.5) = Original Length
5 = Original Length
Therefore, the length of the original piece of wood is 5 feet.