When substituting 1 cup of my 2 1/2 cups of flour in my carrot cake with organic pancake mix Annie's Brand will I still need to add my 4 eggs?

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Looking at the ingredients for Annie's organic pancake mix, it contains flour, sugar, oil, baking powder, and salt. These are the ingredients to consider reducing in your recipe, along with anything that corresponds closely in function (other fats, other sweeteners, baking soda). If we didn't have the ingredients list, we could still rule out eggs because the pancake recipe says to add your own.

There's no way to know what quantities it contains of any of these. You could try to reverse engineer it by looking at one or more similar pancake recipes (containing the same ingredients plus the added milk and egg). Or you could take a wild guess. Don't forget to increase the amount of pancake mix so the amount of flour, not volume, is roughly correct, and reduce everything else accordingly, making up for other losses like moisture.

All things considered though, you should probably just run to the store for flour.

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