To find the total number of plates shipped, we can set up the equation based on the percentage of broken plates:
Let \( x \) be the total number of plates shipped.
According to the problem, 13% of the plates arrived broken, which can be expressed as:
\[ 0.13x = 117 \]
To find \( x \), we can solve the equation:
\[ x = \frac{117}{0.13} \]
Calculating this gives:
\[ x = 900 \]
Thus, the total number of plates shipped is 900.