To address the problem, let’s begin with Part A.
Part A:
We're given the information that a recipe uses a certain amount of milk for each batch of muffins, but we need to quantify that. Assuming the recipe uses \( \frac{1}{2} \) cup of milk for each batch (this example will help illustrate the calculations, but you can replace \( \frac{1}{2} \) with any other specific quantity of milk as needed), let's analyze the statements.
Given \( \frac{1}{2} \) cup of milk per batch:
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If each batch makes 12 muffins, then:
- Each muffin uses \( \frac{1}{2} \div 12 = \frac{1}{24} \) cup of milk.
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For 6 muffins:
- Each muffin uses \( \frac{1}{2} \div 6 = \frac{1}{12} \) cup of milk.
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For 1 muffin:
- Each muffin uses \( \frac{1}{2} \div 1 = \frac{1}{2} \) cup of milk.
Based on this approximation:
- Statement A: \( \frac{1}{24} \) cup of milk is used to make each muffin. (True, if using \( \frac{1}{2}\) cup and making 12 muffins.)
- Statement B: \( \frac{1}{12} \) cup of milk is used to make each muffin. (True, if using \( \frac{1}{2}\) cup and making 6 muffins.)
- Statement C: \( \frac{1}{6} \) cup of milk is used to make each muffin. (False under previous assumptions.)
- Statement D: 1 cup of milk is used to make every 6 muffins. (If the recipe were for 1 cup of milk per 12 muffins, then this would be false.)
- Statement E: 1 cup of milk is used to make every 12 muffins. (True, if using this ratio.)
- Statement F: 1 cup of milk is used to make every 24 muffins. (False under previous assumptions as well.)
Selected Correct Answers:
- A (if using \( \frac{1}{2} \) cup and making 12 muffins)
- B (if using \( \frac{1}{2} \) cup and making 6 muffins)
- E (if using 1 cup for 12 muffins)
Part B:
To find out how many batches of muffins can be made using one gallon of milk, we first note that:
- 1 gallon = 16 cups.
Now, assuming we have established that one batch uses \( \frac{1}{2} \) cup:
- Number of batches = Total cups of milk ÷ Cups per batch
- Number of batches = \( 16 \text{ cups} \div \frac{1}{2} \text{ cup per batch} = 16 \times 2 = 32 \) batches.
Final Answer for Part B: You can make 32 batches of muffins using 1 gallon of milk if each batch uses \( \frac{1}{2} \) cup of milk. Adjust the calculations if the initial cup measurement for the recipe differs!