3. The train departed from the initial station with a certain number of passengers. At the next three stations, passengers disembarked in the following order: $\frac{1}{8}$ of the passengers, then $\frac{1}{7}$ of the remaining passengers, and then $\frac{1}{6}$ of the remaining passengers. After that, 105 passengers remained in the train. No passengers boarded at the stations. How many passengers departed with the train from the initial station?
First method:

Solving backwards.

There are 105 passengers left in the train after $\frac{1}{6}$ of the remaining passengers got off at the third station.

This means that 105 passengers make up $\frac{5}{6}$ of the passengers who remained in the train after the second station.

$105 \cdot 6: 5=126$

After the second station, there were 126 passengers left in the train.

This means that 126 passengers make up $\frac{6}{7}$ of the passengers who remained in the train after the first station.

$126 \cdot 7: 6=147$

After the first station, there were 147 passengers left in the train.

This means that 147 passengers make up $\frac{7}{8}$ of the passengers who boarded at the initial station.

$147 \cdot 8: 7=168$

168 passengers boarded at the initial station.