The answer is 15. The first person bought half of the 15 eggs which is 7½ eggs and another ½ egg. So he bought 8 eggs in total and Jack is left with 7 eggs. The second person bought half of the remaining 7 eggs which is 3½ eggs and another ½ egg. So he bought 4 eggs and Jack is left with 3 eggs. The last person bought half of the remaining 3 eggs which is 1½ eggs and another ½ egg. So the last person bought 2 eggs. That leaves 1 egg remaining in Jack's basket.