A 29 ft board is cut into three pieces at a sawmill. The second piece is 3 ft longer than the first, and the third piece is 2 ft longer than the second. What are the lengths of the three pieces.

The answer to your question is Piece 1 = 7 ft, Piece 2 = 10 ft, Piece 3 = 12 ft

Step-by-step explanation:

Data

total length = 29 ft

1st piece = x

2nd piece = x + 3

3rd piece = 2nd piece + 2 ft

Process

1.- Write the length of the pieces in terms of x

piece 1 = x

piece 2 = x + 3

piece 3 = (x + 3) + 2

2.- Write an equation to find x

         piece 1 + piece 2 + piece 3 = 29

Substitution

                x  +  x + 3 + (x + 3)  + 2 = 29

Solve for x

               x + x + 3 + x + 3 + 2 = 29

               3x = 29 - 3 - 3 - 2

               3x = 29 - 8

               3x = 21

                 x = 21/3

                 x = 7

3.- Find the length of each piece

Piece 1 = 7 ft

Piece 2 = 7 + 3 = 10 ft

Piece 3 = 7 + 3 + 2 = 12 ft

the length of the first piece is 7ft.

the length of the second piece is 10ft.

the length of the third piece is 12ft.

Step-by-step explanation:

Let x represent the length of the first piece.

Let y represent the length if the second piece.

Let z represent the length if the third piece.

A 29 ft board is cut into three pieces at a sawmill. This means that

x + y + z = 29 - - - - - - - - - - -1

The second piece is 3 ft longer than the first. This means that

x = y - 3

The third piece is 2 ft longer than the second. This means that

z = y + 2

Substituting x = y - 3 and z = y + 2 into equation 1, it becomes

y - 3 + y + y + 2 = 29

y + y + y - 3 + 2 = 29

3y = 29 + 1 = 30

y = 30/3

y = 10

x = y - 3 = 10 - 3

x = 7

z = y + 2 = 10 + 2

z = 12