Question

Ari has 10 boards that are each 7.8 ft long. He plans to cut as many pieces as he can from the boards to make some siding for the porch. Each piece needs to be 2.25 ft long.

(a) What is the total length of all the boards that Ari has? Explain how you know.
(b) Each piece of wood for the porch has to be 2.25 ft long. • How many pieces can Ari cut from the 10 boards? • Use words and numbers to explain how you found your answer.
(c) Ari takes the 10 pieces that were left from each board after he cut the 2.25 ft long boards. He lays them end to end on the ground. • What is the total length of the 10 pieces? • Use words and numbers to explain how you found your answer.

Answer 1

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 .

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 = (78)/(2.25)`

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 = (7.8)/(2.25)`

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 .