Final answer:
To determine how many dozen cookies the baker initially made, we add the dozens he sold to the dozens he has left, totaling 9 and 5/6 dozen. However, this does not match any of the answer options provided, indicating a possible error in the question details or options given.
Step-by-step explanation:
Dealing with adding and subtracting fractions and understanding the concept of a dozen. To solve this problem, we need to total the amount of cookies the baker sold and the amount left to determine how many dozen he made initially.
The baker sold 2 and 3/4 dozen plus 3 and 1/2 dozen. To find the total dozens sold, we first convert the mixed numbers to improper fractions: 2 and 3/4 becomes 11/4, and 3 and 1/2 becomes 7/2. Adding these together (11/4 + 7/2), we get 22/4 or 5 and 1/2 dozen sold in total.
The baker still has 4 and 1/3 dozen, or 13/3 dozen, left. Added to the 5 and 1/2, or 11/2 dozen, sold gives us the total original number of dozens. Adding the two amounts together, we have 11/2 + 13/3 = 33/6 + 26/6 = 59/6, which simplifies to 9 and 5/6 dozen. This is not an answer option provided, which suggests there might have been a mistake in the provided options or the student's recounting of the problem.