Analysis: No matter how many times the rope is wound, the total length of the rope is constant. According to the total length, the equation must be listed to calculate the rope length, and the number of meters left after eight laps can be further calculated.

Solution: let the tree circle x meters, that is, the cross-sectional circumference of the tree is x meters.

10X+3= 12X-3

12X- 10X=3+3

2X=6

X=3

Total length of rope: 3× 10+3=33 (m)

Remaining after eight laps: 33-8×3=9 (m).

Answer: About 8 laps, there are 9 meters left.