Question

A carpenter is working on a project that calls for three pieces of wood.
The longest piece must be twice the length of the middle-sized piece.
The shortest piece must be 6 inches shorter than the middle-sized piece.
If the three pieces sum to a total of 80 inches, how long must each piece be?

Let x= length of the middle-sized piece

Write an expression involving x for the length of each piece.

Longest piece =

Middle-sized piece =

Shortest piece =

Write an equation taking the sum of the three pieces and solve.

Answer 1

Longest piece = 2x
Middle-sized piece = x
Shortest piece = x - 6

The equation for the sum of the three pieces is:
2x + x + (x - 6) = 80

Simplifying the equation:
4x - 6 = 80
4x = 86
x = 21.5

Therefore, the length of the middle-sized piece is 21.5 inches.
The longest piece is 2 * 21.5 = 43 inches.
The shortest piece is 21.5 - 6 = 15.5 inches.