A47 foot board is cut into two pieces. if one piece has a length of x feet, what is the length, in feet, of the other piece?

Careful, this could be a trick question. If the board is cut legthwise then both boards would have an equal length of 47 feet. x=y, x=47, y=47.

However if the cut it made along the width, essentially shortening the original board then x is reduced by y (the length of the other piece).
x = 47 - y
Solve for y
x = 47 - y
+y +y
x+y = 47
-x -x
y = 47 - x
(The exact width is unknown, just that we know the width of the other board is less than 47 feet, and if added to the length of the original board it would equal 47 feet.)