I sawed a piece wood in three pieces the ratio is 1:3:6, the longest piece is 2.5 feet longer than the shortest piece. How do I use the draw a diagram strategy to find the length of the original piece?

Answer

2.777 feet.

Sketch three boxes of equal width and label them 1, 3, and 6 to represent the ratios.
Label the shortest piece as x.
Label the longest piece as x + 2.5.
From the diagram, you can see that you have 1 + 3 + 6 = 10 parts.
Write the proportion, where x is the shortest piece: 1/10 = x / (x + 2.5) + 3/10 = 3x / (x + 2.5) + 6/10 = 6x / (x + 2.5).
Solve for x in the equation 1/10 = x / (x + 2.5).
1/10 = x / (x + 2.5) becomes 10x = x + 2.5.
Combine like terms to get 9x = 2.5.
Divide both sides by 9 to get x = 0.2777 (rounded to four decimal places).
The length of the original piece is the sum of the three pieces, or x + 3x + 6x = 10x.
Substitute the value of x to get 10(0.2777) = 2.777 feet.