Final answer:
The question involves the application of ratios and proportions in cooking, specifically when scaling recipes for making batter. Key information is missing regarding the specific ratio of buttermilk batter to liquid eggs, but one could use similar proportional calculations as in the pancake examples provided.
Step-by-step explanation:
The question is related to a mathematics problem involving proportions and ratios. When creating a batter for omelets or pancakes, it is essential to maintain the correct ratios of ingredients to ensure the desired outcome.
In the examples provided, the use of eggs, vegetable oil, pancake mix, and milk are all important factors that are used to determine how many batches of pancakes can be made. The proportions must be scaled up or down based on the quantity of one ingredient to maintain the recipe's integrity.
Unfortunately, the original question about adding buttermilk batter from a Belshaw gun to 1 gallon of liquid eggs lacks required information about the proportion of buttermilk batter to be added for making an omelet batter. However, in general, a similar approach to the pancake batter could be used, where ingredient ratios are kept consistent as the quantity is scaled.