When everyone left for the great annual picnic, each vehicle carried exactly the same number of people. In the middle of the road, ten of the vehicles broke down, so that each of the remaining ones had to take one more person.

On the way home fifteen more vehicles broke down, so that during the return trip there were three more people in each vehicle than when leaving in the morning.

**How many people attended the great annual picnic?**

#### Solution

**900 hikers** They went to the picnic in 100 vehicles, 9 in each. When 10 vehicles broke down, 90 people had to be distributed in the remaining 90 vehicles so that each one was now occupied by 10 people. On the way home, 15 more vehicles broke down, so the 150 people who occupied them had to be distributed among the 75 remaining vehicles that were now occupied by 12 people each, 3 more than at the start of the trip.