Answer:
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
Answer: 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
