To find the total number of plates shipped, we can start by defining the total number of plates shipped as \( x \). According to the problem, 13% of the plates arrive broken, and we know that 117 plates arrived broken.
We can represent this relationship with the equation:
\[ 0.13x = 117 \]
To solve for \( x \), we can rearrange this equation:
\[ x = \frac{117}{0.13} \]
Next, let's analyze the provided equations to see which one matches our approach:
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StartFraction 13 times 100 Over 117 times 100 EndFraction = StartFraction 1300 Over 11,700 EndFraction
- This equation seems to incorrectly represent the relationship.
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StartFraction 117 divided by 1 Over 13 divided by 1 EndFraction = StartFraction 117 Over 13 EndFraction
- This equation can be reinterpreted as \(\frac{117}{0.13}\) if you simplify \( \frac{13}{100} \) into a fraction related to the number of broken plates.
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StartFraction 13 times 9 Over 100 times 9 EndFraction = StartFraction 117 Over 900 EndFraction
- This equation does not correctly reflect the total number of plates.
So, the best representation in terms of finding \( x \) in the context of the problem is the second option. Therefore, the equation you can use to find the total number of plates shipped is:
\[ x = \frac{117}{0.13} \]
While that specific formulation isn't listed, the equivalent in fraction form (which correlates to the second choice using \( \frac{117}{\frac{13}{100}} \) simplifies to \( \frac{117 \times 100}{13} \), which ultimately leads to the correct solution). The second option involving the division works well in arriving at our solution.