To find the total number of glass plates shipped, we can use the information that 13% of the plates arrived broken and that 117 plates were broken.
Let \( x \) be the total number of plates shipped. According to the problem, 13% of \( x \) equals 117. We can express this mathematically as:
\[ 0.13x = 117 \]
To solve for \( x \), divide both sides by 0.13:
\[ x = \frac{117}{0.13} \]
Now, calculating that:
\[ x = 900 \]
Therefore, the total number of plates shipped is 900.