math
posted by Dell on .
A floorfinishing machine uses bars of wax. Once the bar is worn down to 1/2 its original size, it must be replaced with a new bar. Only fullsize bars can be put in the machine. The pieces are melted and recycled to make fullsize bars. If you buy 24 bars and recycle all the pieces, how many fullsize bars can you use? How much wax will be left over? Your goal is to have as little wasted wax as possible.

1st cycle:
equivalent of 12 bars used, 24 halfbars left over
recycled to make 12 new bars
2nd cycle:
equivalent of 6 bars used, 12 halfbars left over
recycled to make 6 new bars
3rd cycle:
equivalent of 3 bars used, 6 halfbars left over
recycled to make 3 new bars
4th cycle:
equivalent of 1.5 bars used, 3 halfbars left over
recycled to make 1.5 new bars
since only fullsize bars can be used, only one more bar can be used
total used: 12+6+3+1.5+1 = 23.5
So 1/2 bar is left over. 
thanks for your help.