Can you tell how many people attended the great annual picnic?

Question

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 can you tell how many people attended the great annual picnic?

Answer 1

900 people
.
They started with x wagons carrying y people each.
Total people = x*y
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After losing 10 wagons, they had (x-10) wagons, carrying (y+1) people each.
Total people = (x - 10) * (y + 1)
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On the way back, they had (x-25) wagons, carrying (y+3) people each.
Total people = (x - 25) * (y + 3)
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(x - 10) * (y + 1) = (x - 25) * (y + 3) => 2x = 15y + 65
x = 7.5y + 32.5
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y = 9, x = 100