Final answer:
Yes, there is missing information in the problem and the number of plates cannot be determined accurately. However, the maximum number of plates can be determined based on the given information.
Step-by-step explanation:
a) Yes, there is missing information in this problem. We are not given the number of bagels of each type on the plate. Without that information, we cannot accurately determine the number of plates.
b) Since we don't know the number of plates, we cannot determine the exact number of plates Dr. Draxton had. However, we can determine the maximum number of plates she could have had by dividing the total number of bagels (180) by the capacity of each plate (16). Therefore, she could have had a maximum of 11 plates of bagels.