If the farmers sold a, b and c chickens before lunch, and the price decreased by d then it's easy to write down the equations and arrive at the following equiva

If the farmers sold a, b and c chickens before lunch, and the price decreased by d then it's easy to write down the equations and arrive at the following equivalency: (a + b - c) * d = 3500 cents Since those are all integers, (a + b - c) must be a divisor of 3500. It must also be positive and <= 26. So it can possibly be 1, 2, 4, 5, 7, 10, 14, 20, 25. For each of these choices just solve a system of 2 linear equations to get the solution. For example if a + b - c = 1 then d = 3500 and the price after lunchtime has to be 0. So they each sold exactly 1 chicken before lunchtime for $35 and gave away all the other chickens for free. It adds up! Checking of the other solutions is left as an excercise to the reader.