Question

a fruit bowl contains only apples and oranges. the ratio of apples to oranges is 2:3. what percentage of the fruits in the bowl are oranges?

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Part-to-Whole Ratios",
"Geometric Percentages"
],
"current_concepts": [
"Ratio Word Problems",
"Part-to-Whole Ratios",
"Geometric Percentages"
]
}
</pre_analysis>

<reasoning>

Determine the part-to-whole ratio for oranges

\[
\text{Ratio of apples to oranges} = 2:3
\]
\[
\text{Total parts} = 2 + 3 = 5
\]
\[
\text{Fraction of oranges} = \frac{3}{5}
\]

Convert the fraction to a percentage

\[
\text{Percentage of oranges} = \frac{3}{5} \times 100\% = 60\%
\]
</reasoning>

<answer>
\(60\%\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Ratio Word Problems"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Part-to-Whole Ratios",
"Geometric Percentages"
],
"current_concepts": [
"Ratio Word Problems",
"Part-to-Whole Ratios",
"Geometric Percentages"
]
}
</pre_analysis>

<reasoning>

Determine the part-to-whole ratio for oranges

\[
\text{Ratio of apples to oranges} = 2:3
\]
\[
\text{Total parts} = 2 + 3 = 5
\]
\[
\text{Fraction of oranges} = \frac{3}{5}
\]

Convert the fraction to a percentage

\[
\text{Percentage of oranges} = \frac{3}{5} \times 100\% = 60\%
\]
</reasoning>

<answer>
\(60\%\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Ratio Word Problems"
]
}
</post_analysis>