Question

in one country, residents were asked to name their primary language. the ratio of residents who said french to those who said punjabi was 110 to 7. if there were 7,260,000 residents who said french, about how many thousands of residents said punjabi?

Explanation:

<pre_analysis>
{
"quality": "clear",
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"step_cot",
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"concepts_used": [
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"Ratio Word Problems"
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</pre_analysis>

<reasoning>

Set up the proportion using the given ratio

\[
\frac{\text{French}}{\text{Punjabi}} = \frac{110}{7}
\]

Solve for the number of Punjabi speakers

\[

$$\begin{aligned} \frac{7,260,000}{x} &= \frac{110}{7} \\ 110x &= 7,260,000 \times 7 \\ 110x &= 50,820,000 \\ x &= 462,000 \end{aligned}$$

\]

Convert the total count to thousands of residents

\[
\frac{462,000}{1,000} = 462
\]
</reasoning>

<answer>
In one country, residents were asked to name their primary language. The ratio of residents who said French to those who said Punjabi was 110 to 7. If there were 7,260,000 residents who said French, about how many thousands of residents said Punjabi? <blank>462</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Ratio Word Problems"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
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"Proportional Reasoning",
"Ratio Word Problems"
],
"new_concepts": [],
"current_concepts": [
"Proportional Reasoning",
"Ratio Word Problems",
"Unit Conversion"
]
}
</pre_analysis>

<reasoning>

Set up the proportion using the given ratio

\[
\frac{\text{French}}{\text{Punjabi}} = \frac{110}{7}
\]

Solve for the number of Punjabi speakers

\[

$$\begin{aligned} \frac{7,260,000}{x} &= \frac{110}{7} \\ 110x &= 7,260,000 \times 7 \\ 110x &= 50,820,000 \\ x &= 462,000 \end{aligned}$$

\]

Convert the total count to thousands of residents

\[
\frac{462,000}{1,000} = 462
\]
</reasoning>

<answer>
In one country, residents were asked to name their primary language. The ratio of residents who said French to those who said Punjabi was 110 to 7. If there were 7,260,000 residents who said French, about how many thousands of residents said Punjabi? <blank>462</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Ratio Word Problems"
]
}
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