Michael's father brought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal size lengths for his shelves.

The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board?

The size of the cut will not, of course, change the
length of the board. It will, of course, affect the total length of the cut pieces, since 1.25" will be lost after 10 cuts.

I don't understand because then it asks :What will the exact length of each shelf be? So, i don't know what I'm supposed to do what numbers to use and how to use those numbers?

Thank you for helping me

Ten cuts produce eleven pieces. The two end pieces will only be affected on one end while the interior pieces will be affected on both ends.

Without the effect of the blade, the pieces would all be:
16/11 ft = 1.455 ft.
The two end pieces will be reduced by half of the blade width (remember: each cut is shared between the two pieces that result; hence the factor of 1/2):
1.455 ft - 0.063 ft = 1.392 ft.
The remaining pieces will be reduced by one blade width, a half width on either side:
1.455 ft - 0.125 ft = 1.330 ft
Thus, two shelves will be 0.062 ft shorter the the remaining nine. 0.062 ft = 0.744 inches. Perhaps the carpenter can make adjustments for this if he knows a little more algebra! :-)
QED

To determine the exact length of each shelf, we need to subtract the total amount lost from the original length of the board.

First, let's calculate the total amount lost from the board after 10 cuts. The saw blade changes the length of the board by -0.125 inches for each cut. So, the total amount lost after 10 cuts would be:

-0.125 inches x 10 cuts = -1.25 inches

Next, we subtract the total amount lost from the original length of the board:

16 feet = 16 feet x 12 inches/foot = 192 inches

192 inches - 1.25 inches = 190.75 inches

Finally, we divide the adjusted length of the board by the total number of shelves Michael plans to cut (which is 11) to find the exact length of each shelf:

190.75 inches / 11 shelves = 17.34 inches (rounded to two decimal places)

Therefore, the exact length of each shelf will be approximately 17.34 inches.

To find the exact length of each shelf, we need to consider the initial length of the board and the number of cuts that will be made. Here's how you can determine the length of each shelf:

1. Start with the initial length of the board: 16 feet.
2. Convert the length of the board to inches for easier calculations. Since there are 12 inches in a foot, the board initially measures 16 feet * 12 inches/foot = 192 inches.
3. Determine the total length that will be lost due to the cuts. Each cut reduces the length of the board by 0.125 inches. So for 10 cuts, the total length lost will be 10 cuts * 0.125 inches/cut = 1.25 inches.
4. Subtract the total length lost from the initial length of the board to find the total length of the cut pieces. 192 inches - 1.25 inches = 190.75 inches.
5. Divide the total length of the cut pieces by the number of shelves to find the exact length of each shelf. 190.75 inches / 11 shelves = 17.34 inches (rounded to two decimal places).

Therefore, the exact length of each shelf will be approximately 17.34 inches.