The following surprisingly difficult challenge problem was given to the students at my son's Math Circle last week.  Unlike the three princesses puzzle in my previous post, this one does require a bit of pen and paper to solve; I spent more than fifteen minutes on the problem, during half of which I was convinced the problem was ill-posed.  Remarkably, one of the students in the class actually solved it in class time (not my son, though).

As before, I would prefer if you not simply spoil the answer in comments, but instead discuss your thought processes in how you arrived at your solution.

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Three farmers were selling chickens at the local market.  One farmer had 10 chickens to sell, another had 16 chickens to sell, and the last had 26 chickens to sell.  In order not to compete with each other, they agreed to all sell their chickens at the same price.  But by lunchtime, they decided that sales were not going so well, and they all decided to lower their prices to the same lower price point.  By the end of the day, they had sold all their chickens.  It turned out that they all collected the same amount of money, $35, from the day's chicken sales.  What was the price of the chickens before lunchtime and after lunchtime?
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