Question

a restaurant offers 5 appetizers, 9 entrees, and 7 desserts. how many full meals (1 of each) can be created?

number of meals = ?

Explanation:

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<reasoning>

Identify the choices for each meal course

\[

$$\begin{aligned} &\text{Appetizers } (A) = 5 \\ &\text{Entrees } (E) = 9 \\ &\text{Desserts } (D) = 7 \end{aligned}$$

\]

Apply the fundamental counting principle

\[

$$\begin{aligned} \text{Total Meals} &= A \times E \times D \\ &= 5 \times 9 \times 7 \\ &= 45 \times 7 \\ &= 315 \end{aligned}$$

\]
</reasoning>

<answer>
A restaurant offers 5 appetizers, 9 entrees, and 7 desserts. How many full meals (1 of each) can be created?

Number of Meals = <blank>315</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fundamental Counting Principle"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
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"step_cot",
"blank_filling_formatter",
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<reasoning>

Identify the choices for each meal course

\[

$$\begin{aligned} &\text{Appetizers } (A) = 5 \\ &\text{Entrees } (E) = 9 \\ &\text{Desserts } (D) = 7 \end{aligned}$$

\]

Apply the fundamental counting principle

\[

$$\begin{aligned} \text{Total Meals} &= A \times E \times D \\ &= 5 \times 9 \times 7 \\ &= 45 \times 7 \\ &= 315 \end{aligned}$$

\]
</reasoning>

<answer>
A restaurant offers 5 appetizers, 9 entrees, and 7 desserts. How many full meals (1 of each) can be created?

Number of Meals = <blank>315</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fundamental Counting Principle"
]
}
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