Answer:
The total length of the board is 78 ft.
The number of pieces of wood for porch cut from the boards be 34 .
Total length of left 10 pieces that were left from each board after he cut the 2.25 ft long boards be 10.5 ft .
Step-by-step explanation:
Case (a)
As given
Ari has 10 boards that are each 7.8 ft long.
Total length of board = Total number of board × Length of each board
Putting the values in the above
Total length of board = 10 × 7.8
= 78 ft
Therefore the total length of the board is 78 ft.
Case (b)
As given
Each piece of wood for the porch has to be 2.25 ft long.
Total length of the 10 board = 78 ft
Let us assume that the number of piece of wood for porch cut from board be x.
Than the equation becomes
2.25 × x = 78
x = 34.7 (Approx)
Thus
x = 34
Therefore the number of pieces of wood for porch cut from the boards be 34 .
Case (c)
As given
As the length of the one board be 7.8 ft and the length of the each piece of wood for porch is 2.25 ft .
Let us assume that the number of piece of wood for porch cut from one board be y .
Than the equation becomes
y × 2.25 = 7.8
y = 3.5 (Approx)
y = 3
Thus the number of piece of wood for porch cut from one board be 3 .
Than
Length of piece left after cutting 2.25 ft piece of wood from each board = Length of each boards - Number of pieces of wood × Length of each pieces of wood.
Length of piece left after cutting 2.25 ft piece of wood from each board = 7.8 - 3 × 2.25
= 7.8 - 6.75
= 1.05 ft
Thus
Total length of left 10 pieces = 10 × Length of piece left after cutting 2.25 ft piece of wood from each board
= 10 × 1.05
= 10.5 ft
Therefore total length of left 10 pieces that were left from each board after he cut the 2.25 ft long boards be 10.5 ft .