Final answer:
To keep the same unit rate of sugar and flour in a single batch, you need to match the correct amount of sugar to the correct amount of flour. The correct matches are 4.5 cups of sugar with 6.75 cups of flour and 8 cups of sugar with 12 cups of flour.
Step-by-step explanation:
To keep the same unit rate of sugar and flour in a single batch, you need to match the correct amount of sugar to the correct amount of flour. The unit rate is determined by the ratio of sugar to flour. In this case, the unit rate is 2 cups of sugar to 3 cups of flour.
Let's consider the options provided:
- 11.5 cups of flour - This doesn't match with any amount of sugar
- 4.5 cups of sugar - This matches with 6.75 cups of flour (since 4.5/6.75 = 2/3)
- 12 cups of flour - This doesn't match with any amount of sugar
- 5 cups of sugar - This doesn't match with any amount of flour
- 11.25 cups of flour - This doesn't match with any amount of sugar
- 7.5 cups of sugar - This doesn't match with any amount of flour
- 8 cups of sugar - This matches with 12 cups of flour (since 8/12 = 2/3)
- 4 cups of sugar - This doesn't match with any amount of flour
So, the correct matches are:
4.5 cups of sugar with 6.75 cups of flour
8 cups of sugar with 12 cups of flour