Solution:
To determine the unit price of a dozen and a half eggs that cost $4.65, we need to first calculate the total number of eggs in a dozen and a half, and then divide the total cost by the number of eggs.

A dozen refers to 12 items, so a dozen and a half is equal to 12 + 6 = 18 eggs.

To find the unit price, we divide the total cost ($4.65) by the number of eggs (18):

Unit price = Total cost / Number of eggs
Unit price = $4.65 / 18

Calculating this:

Unit price = $0.2583 (rounded to four decimal places)

Therefore, the unit price of a dozen and a half eggs that cost $4.65 is approximately $0.2583 per egg.