Answer
72 people.
Work Step by Step
The volume of water that is displaced when people start getting their feet wet is the full volume of the raft $V_{raft}=12V_{log}=12\pi r_{log}^2L_{log}$.
The buoyant force equals the weight of the water displaced by the full volume of the logs.
$$F_b=V_{raft}\rho_{water}g$$
This equals the weight of the raft plus N passengers.
$$W_{total}= V_{raft}\rho_{wood}g+Nm_{person}= V_{raft}0.60\rho_{water}g+Nm_{person}$$
$$N=\frac{V_{raft}g \rho_{water}(1-0.60)}{m_{person}}=72.97$$
When 73 people are on the raft, their feet will be wet. 72 people can manage to keep their feet dry.