Kenny is wrong. You can make 5.25 batches with 2 5/8 cups of brown sugar. His mistake was underestimating how many batches you can make by not dividing the total brown sugar by the amount needed per batch.
Kenny's mistake: He assumed you could only make a whole number of batches, overlooking the possibility of having leftover brown sugar from the last batch.
Calculating the actual number of batches:
Convert 2 5/8 cups to standard units:
2 5/8 cups = (2 * 8) + 5 / 8 cups = 17/8 cups
Let x be the number of batches you can make.
The amount of brown sugar used per batch (b) needs to be less than or equal to the total available (17/8 cups):
bx ≤ 17/8
Dividing both sides by b reveals the maximum number of batches possible:
x ≤ 17/8b
The recipe you're using will determine the amount of brown sugar needed per batch (b). Let's say the recipe for one batch requires 1/2 cup of brown sugar. Then:
x ≤ 17/8 * (1/2)
x ≤ 17/16 ≈ 1.0625
Since batches are whole units, you can round down 1.0625 to 1, but that would waste some brown sugar. A better option is to round up to the nearest "half batch" to utilize all the available sugar:
x ≈ 1.5
Therefore, with 2 5/8 cups of brown sugar, you can make up to 1.5 batches, not just 10 as Kenny claimed. You could either make 1 full batch and have 3/8 cup leftover, or make 1 full batch and a half batch, using all the brown sugar.
In conclusion, Katie is correct. By properly utilizing the available brown sugar and considering fractional batches, you can make significantly more than what Kenny assumed.