Question

Gina needs to cut a board to use for a project. The board is 10 feet long. She first has to cut off 112 feet from one end of the board. She then cuts the remaining section of board into 3 equal pieces.

Answer 1

To find the length of each equal piece from a 10-foot board after cutting 1.5 feet, divide the remaining length (8.5 feet) by 3. The equation representing this is
`\(3x - 1 (1)/(2) = 10\)`.

Gina starts with a 10-foot board.

She cuts off 1.5 feet from one end, leaving
`\(10 - 1.5 = 8.5\)` feet of board.

Let
`\(x\)` represent the length of each of the three equal pieces.

The equation to determine the length of each equal piece is set up as follows:

`\[3x = 8.5\]`

To find the length of each piece, divide the remaining board length by the number of pieces:

`\[x = (8.5)/(3)\]`

Now, let's calculate \(x\):

`\[x = (8.5)/(3) = 2.833 \text{ feet}\]`

So, each of the three equal pieces has a length of approximately 2.833 feet.

The equation
`\(3x = 8.5\)` can be rearranged as
`\(3x - 1 (1)/(2) = 10\)` to represent the scenario where Gina cuts 1.5 feet and wants to determine the total length of the three equal pieces.