To find the total number of plates shipped, we know that 13% of the total plates shipped arrived broken, and that number is given as 117. We can use this information to set up the equation.
Let \( x \) be the total number of plates shipped. Then the relationship can be expressed as:
\[ 0.13x = 117 \]
To find \( x \), you can rearrange the equation:
\[ x = \frac{117}{0.13} \]
Now, let's examine the options given to see which corresponds to this scenario:
-
Option: \( \frac{13 \times 100}{117 \times 100} = \frac{1300}{11700} \)
This option represents a simplification of the proportion. It is not the correct equation to directly find the total number of plates, but rather a ratio.
-
Option: \( \frac{117}{1} \div \frac{13}{1} = \frac{117}{13} \)
This option simplifies to the same division as in the equation \( 0.13x = 117 \). This is a valid equation and can lead to finding \( x \).
-
Option: \( \frac{13 \times 9}{100 \times 9} = \frac{117}{900} \)
This option does not correctly represent our problem.
-
Option: \( \frac{100}{13} \div \frac{117}{13} = \frac{7.7}{9} \)
This also does not correspond directly to our main equation.
The best choice from the provided options that represents the relationship for finding the total number of plates shipped (by solving \( 0.13x = 117 \) or rearranging to find \( x \)) is:
\[ \frac{117}{13} \]
This can lead to the total number of plates shipped. Thus, the appropriate choice is:
Option 2: \( \frac{117}{13} \).