a carpenter divides a board that is 3.5 inches wide into 4 pieces of equal widthby cutting 3 places. if the width of her saw blade is 1/8 inch, what is the finished width of each piece? What percent of the board length is actullay used?
To divide the board into 4 equal pieces, the carpenter will need to make 3 cuts. Since each cut removes the width of the saw blade, the actual width used for each cut will be 3.5 inches - 1/8 inch.
Thus, each piece will have a finished width of (3.5 inches - 1/8 inch) / 4.
To calculate this, let's simplify the fraction: 1/8 inch = 0.125 inches.
Therefore, each piece will have a finished width of (3.5 inches - 0.125 inches) / 4.
Simplifying further, each piece will have a finished width of 3.375 inches / 4.
To find the actual percentage of the board's length used, we need to calculate the sum of the finished widths and divide it by the original width of the board.
The sum of the finished widths is 3.375 inches x 4 pieces = 13.5 inches.
Now, let's calculate the percentage of the board length used: (13.5 inches / 3.5 inches) x 100%.
Using a calculator: (13.5 / 3.5) x 100% = 385.71%.
Therefore, each piece will have a finished width of 0.84375 inches (rounded to 5 decimal places), and the actual percentage of the board length used is approximately 385.71%.
To find the finished width of each piece, we can start by determining the total length of the cuts made by the saw. Since the carpenter cuts the board in three places, there will be a total of four pieces.
First, we need to subtract the width of the saw blade from the width of the board to find the usable width. The usable width is:
3.5 inches - 3 * (1/8 inch) = 3.5 inches - 3/8 inch = 3.5 inches - 0.375 inches = 3.125 inches.
Next, we divide the usable width by four to find the finished width of each piece:
3.125 inches / 4 = 0.78125 inches.
So, the finished width of each piece is approximately 0.78125 inches.
To find the percent of the board length actually used, we can divide the combined width of the four pieces by the original width of the board and multiply by 100.
The combined width of the four pieces is 4 * 0.78125 inches = 3.125 inches.
To find the percent used, we divide 3.125 inches by the original width of the board (3.5 inches) and multiply by 100:
(3.125 inches / 3.5 inches) * 100 = 0.892857 * 100 = 89.2857 (rounded to four decimal places).
So, approximately 89.2857% of the board length is actually used.