How Many Servings?

Demetrius and BJ are arguing about the answer they got when posed with the following question:

One serving of Sweetened Tasty Crisp cereal is ¾ cup. I ate 1¼ cups of Sweetened Tasty Crisp for breakfast. How many servings did I eat?

BJ claims that there are almost 2 servings, but point out that they are short ¼ cup, so the answer is 1 ¾ servings because ¾ is ¼ less than a whole.

Demetrius says that the answer is 1 2/3 servings because there was one entire ¾ cup serving and 2 of the 3 parts it would take to make another full serving.

Help them!

(Source: Adapted from Mathematics for Elementary Teachers, Sybilla Beckman, 2nd ed., 2008)