Part A
To determine which statements are true about the amount of milk used per muffin, we need to know how much milk is used in total for the batch as well as how many muffins are made in that batch.
Let's denote:
- The amount of milk used per batch: \( x \) cups,
- The number of muffins made per batch: \( n \) muffins.
Since the problem doesn't specify the exact amount of milk used in the recipe or how many muffins it produces, we cannot definitively calculate how much milk is used per muffin. However, if we had to analyze the statements, we can assume certain values.
Given the clues in the multiple-choice answers:
- It seems that the fractions are meant to represent the amount of milk per muffin.
Let’s analyze each option based on hypothetical assumptions:
A. \( \frac{1}{24} \) cup of milk per muffin: This would imply a specific total amount of milk divided by muffins.
B. \( \frac{1}{12} \) cup of milk per muffin: Similar analysis as below.
C. \( \frac{1}{6} \) cup of milk per muffin: Again, similar.
D. \( \frac{1}{6} \) cup of milk used to make every \( 666 \) muffins: \( \frac{1}{6} \) would imply a batch with multiple muffins.
E. \( \frac{1}{12} \) cup of milk used to make every \( 121212 \) muffins: Implies a very large batch.
F. \( \frac{1}{24} \) cup of milk used to make every \( 242424 \) muffins: Implies an extremely large batch.
Without knowing \( x \) or \( n \), we can't definitively select correct statements. However, if we assume the initial recipe that has been used generally, often recipes use proportions that give a favorable serving. Usually, when the amount of milk is small, it might be multiplied deeply based on batches.
To summarize, we do not have enough definitive information to decisively classify any option as true due to unknown variables in the problem.
Part B
If we assume the same batch in the recipe uses \( \frac{1}{2} \) cups of milk:
1 gallon = 16 cups.
If each batch uses \( \frac{1}{2} \) cup of milk, then the number of batches can be calculated as follows:
\( \text{Number of batches} = \frac{\text{Total cups in a gallon}}{\text{cups per batch}} = \frac{16 \text{ cups}}{\frac{1}{2} \text{ cups}} = 16 \times 2 = 32 \text{ batches}. \)
Thus, 32 batches can be made using 1 gallon of milk if each batch uses \( \frac{1}{2} \) cup of milk as an assumption.
Part C
Given that the bakery makes 96 muffins every day for 30 days, we first need to ascertain how many total batches are needed to make 96 muffins.
If we assume the same batch makes a number of muffins, let’s say for simple understanding that it produces \( m \) muffins — We don't have that number, but we can proceed assuming it's the same foundation as before.
If \( n \) (the number of muffins per batch) = 12 muffins (a common proportion):
-
Total muffins made in 30 days = \( 96 \text{ muffins/day} \times 30 \text{ days} = 2880 \text{ muffins}. \)
-
The number of batches needed = \( \frac{2880 \text{ muffins}}{12 \text{ muffins/batch}} = 240 \text{ batches}. \)
Now we can calculate how much milk is needed:
If the recipe uses \( \frac{1}{2} \) cup of milk per batch for calculating or any specified value in proportion:
Total milk needed = \( 240 \text{ batches} \times \frac{1}{2} \text{ cup/batch} = 120 \text{ cups}. \)
Convert cups to gallons:
1 gallon = 16 cups, thus:
\( \frac{120 \text{ cups}}{16 \text{ cups/gallon}} = 7.5 \text{ gallons}. \)
Therefore, the bakery needs a total of 7.5 gallons of milk to make 96 muffins every day for 30 days, assuming the unspecified batch size follows modeled assumptions.
This answer might differ if the batch size or milk amount differs than assumed—adjust calculations accordingly.
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