A baker wants to reduce the amount of sugar in his cake recipes. He decides to reduce the amount used in 1 cake by 1/2 cup. He then uses 4 1/2 cups of sugar to bake 6 cakes.
How much sugar was originally in each cake recipe?

There were 5/4 =1.25 cups of sugar originally in each cake recipe

Step-by-step explanation:

Proportions

Provided each element of a set is identical to the others, there are certain mathematical relations that can be used to estimate and extrapolate possible outcomes.  

We know the baker uses 4 1/2 cups of sugar to bake 6 cakes. This gives us the amount of sugar used to bake each cake:

This happened after the reduction of sugar by 1/2 cup by cake, this means that before the reduction, each cake had

There were 5/4 =1.25 cups of sugar originally in each cake recipe