Question

question 10 of 23 · multiple choice

a two-man carpenter crew sets approximately 725 sq. ft. of concrete forms per day.

if they have erected \\(\frac{2}{5}\\) of this amount how many square feet of forming remain to be done today?

a 1812.5sq.ft.
b 435 sq.ft.
c 1015sq.ft.
d 290sq.ft.

Explanation:

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<reasoning>

Identify the given values and target

We are given:

• Total daily concrete forms: \(725\text{ sq. ft.}\)
• Fraction of forms already erected: \(\frac{2}{5}\)

We need to find the remaining square feet of forming to be done today.

Determine the remaining fraction

Using the Fraction Arithmetic knowledge point, we find the fraction of work that remains:
\[
1 - \frac{2}{5} = \frac{3}{5}
\]

Calculate the remaining square footage

Using the Fraction Arithmetic knowledge point, we multiply the remaining fraction by the total daily amount:
\[
725 \times \frac{3}{5} = 145 \times 3 = 435\text{ sq. ft.}
\]
</reasoning>

<answer>
<mcq-option>(A) 1812.5sq.ft.</mcq-option>
<mcq-correct>(B) 435 sq.ft.</mcq-correct>
<mcq-option>(C) 1015sq.ft.</mcq-option>
<mcq-option>(D) 290sq.ft.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Word Problems"
]
}
</post_analysis>

Answer:

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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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"new_concepts": [
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</pre_analysis>

<reasoning>

Identify the given values and target

We are given:

• Total daily concrete forms: \(725\text{ sq. ft.}\)
• Fraction of forms already erected: \(\frac{2}{5}\)

We need to find the remaining square feet of forming to be done today.

Determine the remaining fraction

Using the Fraction Arithmetic knowledge point, we find the fraction of work that remains:
\[
1 - \frac{2}{5} = \frac{3}{5}
\]

Calculate the remaining square footage

Using the Fraction Arithmetic knowledge point, we multiply the remaining fraction by the total daily amount:
\[
725 \times \frac{3}{5} = 145 \times 3 = 435\text{ sq. ft.}
\]
</reasoning>

<answer>
<mcq-option>(A) 1812.5sq.ft.</mcq-option>
<mcq-correct>(B) 435 sq.ft.</mcq-correct>
<mcq-option>(C) 1015sq.ft.</mcq-option>
<mcq-option>(D) 290sq.ft.</mcq-option>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Word Problems"
]
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