Question

question 18
1 pts
if 5 oz of a solution contains 4 1/2 oz of water, how many oz of water are in 20 oz of solution?

18 oz
20 oz
200 oz
180 oz

Explanation:

<pre_analysis>
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"concepts_used": [
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</pre_analysis>

<reasoning>

Set up the proportion

\[
\frac{4\frac{1}{2}\text{ oz water}}{5\text{ oz solution}} = \frac{x\text{ oz water}}{20\text{ oz solution}}
\]

Solve for the unknown quantity

\[
x = 20 \times \frac{4\frac{1}{2}}{5}
\]

Calculate the final value

\[
x = 4 \times 4\frac{1}{2} = 4 \times \frac{9}{2} = 18\text{ oz}
\]
</reasoning>

<answer>
<mcq-correct>(A) 18 oz</mcq-correct>
<mcq-option>(B) 20 oz</mcq-option>
<mcq-option>(C) 200 oz</mcq-option>
<mcq-option>(D) 180 oz</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Reasoning"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Mixed Number Multiplication",
"Proportional Reasoning"
],
"new_concepts": [],
"current_concepts": [
"Mixed Number Multiplication",
"Proportional Reasoning"
]
}
</pre_analysis>

<reasoning>

Set up the proportion

\[
\frac{4\frac{1}{2}\text{ oz water}}{5\text{ oz solution}} = \frac{x\text{ oz water}}{20\text{ oz solution}}
\]

Solve for the unknown quantity

\[
x = 20 \times \frac{4\frac{1}{2}}{5}
\]

Calculate the final value

\[
x = 4 \times 4\frac{1}{2} = 4 \times \frac{9}{2} = 18\text{ oz}
\]
</reasoning>

<answer>
<mcq-correct>(A) 18 oz</mcq-correct>
<mcq-option>(B) 20 oz</mcq-option>
<mcq-option>(C) 200 oz</mcq-option>
<mcq-option>(D) 180 oz</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Reasoning"
]
}
</post_analysis>