# Math

posted by Maria Sanchez

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?

1. Joe

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

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