Question

the legend on a map states that 1 cm is 15 km. if you measure 12 cm on the map, how many km would the actual distance be?

? km

Explanation:

<pre_analysis>
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"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
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"needs_drawing": false,
"concepts_used": [
"Dimensional Analysis",
"Unit Conversion",
"Cross Multiplication"
],
"new_concepts": [
"Map Scale Calculations"
],
"current_concepts": [
"Dimensional Analysis",
"Unit Conversion",
"Cross Multiplication",
"Map Scale Calculations"
]
}
</pre_analysis>

<reasoning>

Identify the given scale and measurement

Using the Dimensional Analysis and Unit Conversion knowledge points
\[

$$\begin{aligned} &\text{Scale ratio: } \frac{15\text{ km}}{1\text{ cm}}\\ &\text{Measured distance: } 12\text{ cm} \end{aligned}$$

\]

Set up the proportion to solve for the actual distance

Using the Cross Multiplication knowledge point
\[

$$\begin{aligned} &\frac{1\text{ cm}}{15\text{ km}} = \frac{12\text{ cm}}{x\text{ km}}\\ &1 \cdot x = 12 \cdot 15\\ &x = 180 \end{aligned}$$

\]
</reasoning>

<answer>
The legend on a map states that \(1\text{ cm}\) is \(15\text{ km}\). If you measure \(12\text{ cm}\) on the map, how many km would the actual distance be?

<blank>180</blank> km
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Map Scale Calculations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
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],
"needs_drawing": false,
"concepts_used": [
"Dimensional Analysis",
"Unit Conversion",
"Cross Multiplication"
],
"new_concepts": [
"Map Scale Calculations"
],
"current_concepts": [
"Dimensional Analysis",
"Unit Conversion",
"Cross Multiplication",
"Map Scale Calculations"
]
}
</pre_analysis>

<reasoning>

Identify the given scale and measurement

Using the Dimensional Analysis and Unit Conversion knowledge points
\[

$$\begin{aligned} &\text{Scale ratio: } \frac{15\text{ km}}{1\text{ cm}}\\ &\text{Measured distance: } 12\text{ cm} \end{aligned}$$

\]

Set up the proportion to solve for the actual distance

Using the Cross Multiplication knowledge point
\[

$$\begin{aligned} &\frac{1\text{ cm}}{15\text{ km}} = \frac{12\text{ cm}}{x\text{ km}}\\ &1 \cdot x = 12 \cdot 15\\ &x = 180 \end{aligned}$$

\]
</reasoning>

<answer>
The legend on a map states that \(1\text{ cm}\) is \(15\text{ km}\). If you measure \(12\text{ cm}\) on the map, how many km would the actual distance be?

<blank>180</blank> km
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Map Scale Calculations"
]
}
</post_analysis>