Great Picnic Puzzle

The Puzzle:

Great Picnic Puzzle
When they started off on the great annual picnic every wagon in town was pressed into service, each one carrying the same number of people.

Half way to the picnic ground ten wagons broke down, so it was necessary for each of the remaining wagons to carry one more person.

When they started for home it was discovered that fifteen more wagons were out of commission, so on the return trip there were three persons more in each wagon than when they started out in the morning.

Now who can tell how many people attended the great annual picnic?
Do you have the answer? Check against our solution!