Jamie wanted a board cut into 8 equal pieces. The Lucas Lumber Co. charges 60 cents for cutting a board into 4 equal pieces. How much will it charge for cutting Jamie's board? (The teacher said the answer was not $1.20)
One possible answer is "whatever it wants!".
The "mathematical" answer is 90 cents: Lucas Lumber charges
30 cents for a cut, and it takes three cuts to cut a board into
8 equal pieces. How do I know that Lucas Lumbers charges
30 cents for a cut? Well it takes two cuts to cut a board into
four equal pieces, and this costs 60 cents.
To get eight pieces in three cuts first cut the board in half. Put one half on top of the other and cut again to get four pieces. Finally put the four pieces in a stack and cut again to get eight.