Glass plates are packaged and shipped to a retail store, but 13 percent of all the shipped plates arrive broken. In the last shipment, 117 arrive broken. Which equation can be used to find the total number of plates shipped?

StartFraction 13 times 100 Over 117 times 100 EndFraction = StartFraction 1300 Over 11,700 EndFraction
StartFraction 117 divided by 1 Over 13 divided by 1 EndFraction = StartFraction 117 Over 13 EndFraction
StartFraction 13 times 9 Over 100 times 9 EndFraction = StartFraction 117 Over 900 EndFraction

1 answer

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:

  1. StartFraction 13 times 100 Over 117 times 100 EndFraction = StartFraction 1300 Over 11,700 EndFraction

    • This equation seems to incorrectly represent the relationship.
  2. 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.
  3. 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.