Question
(a)
A bakery uses a muffin recipe that uses
cup of milk for every batch of
muffins.
Part A
Based on the recipe, which statement is true?
Select each correct answer.
A
\frac{1}{24}
24
1
cup of milk is used to make each muffin.
B
\frac{1}{12}
12
1
cup of milk is used to make each muffin.
C
frac{1}{6}
6
1
cup of milk is used to make each muffin.
D
1 cup of milk is used to make every 6 muffins.
E
1 cup of milk is used to make every 12 muffins.
F
1 cup of milk is used to make every 24 muffins.
(b)
Part B
How many batches of
muffins can be made using one gallon of milk? Show your work or explain how you found your answer.
Enter your answer and your work or explanation in the box provided.
Answers
GPT-4o mini
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:**
- If each batch makes 12 muffins, then:
- Each muffin uses \( \frac{1}{2} \div 12 = \frac{1}{24} \) cup of milk.
- For 6 muffins:
- Each muffin uses \( \frac{1}{2} \div 6 = \frac{1}{12} \) cup of milk.
- 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!
### 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:**
- If each batch makes 12 muffins, then:
- Each muffin uses \( \frac{1}{2} \div 12 = \frac{1}{24} \) cup of milk.
- For 6 muffins:
- Each muffin uses \( \frac{1}{2} \div 6 = \frac{1}{12} \) cup of milk.
- 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!