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Mara found the length of time of an investment. The principal of the investment was [tex]\(\$ 4,300\)[/tex], the interest rate was 6.2 percent, and the interest was [tex]\(\$ 2,666\)[/tex]. Mara made an error in her work.

[tex]\[
\begin{aligned}
I & = \text{Prt} \\
2666 & = (4300)(0.062)t \\
2666 & = (266.6)t \\
\frac{2666}{266.6} & = t \\
10 & = t
\end{aligned}
\][/tex]

What was Mara's error?

A. Mara did not substitute the values from the problem into the formula correctly.
B. Mara did not multiply correctly.
C. Mara did not divide correctly.
D. Mara divided when she should have multiplied.



Answer :

GinnyAnswer
Let's analyze Mara's work step by step to identify her error:

1. Formula Setup:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \text{ (prt)} \][/tex]

2. Substitution in the formula:
[tex]\[ 2666 = 4300 \times 0.062 \times t \][/tex]
This step is correctly done by Mara.

3. Multiplying Principal and Rate:
[tex]\[ 2666 = 266.6 \times t \][/tex]
This multiplication is also done correctly.

4. Solving for Time ([tex]\( t \)[/tex]):
Mara's incorrect step:
[tex]\[ \frac{266.6}{2666} = t \][/tex]
Mara divided [tex]\( 266.6 \)[/tex] by [tex]\( 2666 \)[/tex] incorrectly. The correct step should have been:
[tex]\[ t = \frac{2666}{266.6} \][/tex]

Let's see the correct calculation:

Correct Division:

[tex]\[ t = \frac{2666}{266.6} \][/tex]

When computed correctly, [tex]\( t = 10 \)[/tex].

So, Mara's error was in the division step. She wrongly divided [tex]\( 266.6 \)[/tex] by [tex]\( 2666 \)[/tex] instead of dividing [tex]\( 2666 \)[/tex] by [tex]\( 266.6 \)[/tex]. Therefore, the correct answer is:

Mara did not divide correctly.

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