Question

mara found the length of time of an investment. the principal of the investment was \\$4,300, the interest rate was 6.2 percent, and the interest was \\$2,666. mara made an error in her work.

\\i = prt\\
\\2666 = (4300)(0.062)t\\
\\2666 = (266.6)t\\
\\\frac{266.6}{2666} = t\\
\\0.1 = t\\

what was maras error?

mara did not substitute the values from the problem into the formula correctly.
mara did not multiply correctly.
mara did not divide correctly.
mara divided when she should have multiplied.

Explanation:

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<reasoning>

Identify the given values and formula

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} &I = prt\\ &I = 2666,\quad p = 4300,\quad r = 0.062 \end{aligned}$$

\]

Check substitution and multiplication

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} &2666 = (4300)(0.062)t\\ &4300 \times 0.062 = 266.6\\ &2666 = 266.6t \end{aligned}$$

\]

Analyze the division step

To isolate \(t\) in the equation \(2666 = 266.6t\), we must divide both sides by \(266.6\):
\[
t = \frac{2666}{266.6} = 10
\]
Mara wrote:
\[
\frac{266.6}{2666} = t
\]
This is the reciprocal of the correct division. Therefore, Mara did not divide correctly.
</reasoning>

<answer>
<mcq-option>Mara did not substitute the values from the problem into the formula correctly.</mcq-option>
<mcq-option>Mara did not multiply correctly.</mcq-option>
<mcq-correct>Mara did not divide correctly.</mcq-correct>
<mcq-option>Mara divided when she should have multiplied.</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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]
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Answer:

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</pre_analysis>

<reasoning>

Identify the given values and formula

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} &I = prt\\ &I = 2666,\quad p = 4300,\quad r = 0.062 \end{aligned}$$

\]

Check substitution and multiplication

Using the Simple Interest Formula knowledge point
\[

$$\begin{aligned} &2666 = (4300)(0.062)t\\ &4300 \times 0.062 = 266.6\\ &2666 = 266.6t \end{aligned}$$

\]

Analyze the division step

To isolate \(t\) in the equation \(2666 = 266.6t\), we must divide both sides by \(266.6\):
\[
t = \frac{2666}{266.6} = 10
\]
Mara wrote:
\[
\frac{266.6}{2666} = t
\]
This is the reciprocal of the correct division. Therefore, Mara did not divide correctly.
</reasoning>

<answer>
<mcq-option>Mara did not substitute the values from the problem into the formula correctly.</mcq-option>
<mcq-option>Mara did not multiply correctly.</mcq-option>
<mcq-correct>Mara did not divide correctly.</mcq-correct>
<mcq-option>Mara divided when she should have multiplied.</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Algebraic Error Analysis"
]
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