Pet Rocks

The town of Ware has exactly 5000 families. Every family has 0, 1, or 2 pet rocks. Every pet rock belongs to a family. Most families have 1 pet rock. Exactly half of the remaining families have 2 pet rocks. How many pet rocks are there in Ware?


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A lovely problem.

By reasoning: Some families have 1 pet rock. Half of the rest have 2. The other half of the rest have none. If each family having 2 were to give one of them to a family having none, then every family in Ware would have 1 pet rock. So there are 5000 pet rocks in Ware.

By algebra: If n families have 1, then (5000 – n) / 2 have 2. So the number of pet rocks is n + 2(5000 – n) / 2 = n + 5000 – n = 5000.

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