To find the total number of plates shipped, we can use the information given. If 13% of the plates arrived broken and 117 plates are broken, we can set up the following equation:
Let \( x \) be the total number of plates shipped. Since 13% of the plates are broken, we can express this mathematically as:
\[ 0.13x = 117 \]
To find \( x \), we can solve for it by dividing both sides by 0.13:
\[ x = \frac{117}{0.13} \]
Calculating the right side:
\[ x = 900 \]
Therefore, the total number of plates shipped is 900 plates.