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solve each equation: \\\\frac{2.5}{1.25} = \\frac{8}{y}\\ answer exampl…
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Question

solve each equation:

\\\frac{2.5}{1.25} = \frac{8}{y}\\

answer

example: x=3; x=5

Explanation:

Response

<pre_analysis>
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"quality": "clear",
"question_count": 1,
"skills_matched": [
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],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
],
"new_concepts": [],
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</pre_analysis>

<reasoning>

Write down the proportion

\[\frac{2.5}{1.25} = \frac{8}{y}\]

Simplify the left side

\[\frac{2.5}{1.25} = 2\]

Solve for y

\[

$$\begin{aligned} 2 &= \frac{8}{y} \\ 2y &= 8 \\ y &= 4 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 4\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Algebraic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
]
}
</pre_analysis>

<reasoning>

Write down the proportion

\[\frac{2.5}{1.25} = \frac{8}{y}\]

Simplify the left side

\[\frac{2.5}{1.25} = 2\]

Solve for y

\[

$$\begin{aligned} 2 &= \frac{8}{y} \\ 2y &= 8 \\ y &= 4 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 4\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Algebraic Equations"
]
}
</post_analysis>