To find the total number of plates shipped, we can set up the equation based on the information provided:
Let \( x \) be the total number of plates shipped. According to the problem, 20% of the plates arrived broken, which can be expressed as:
\[ 0.20x = 145 \]
To find \( x \), we can divide both sides of the equation by 0.20:
\[ x = \frac{145}{0.20} \]
Calculating that gives:
\[ x = 145 \div 0.20 = 145 \div \frac{1}{5} = 145 \times 5 = 725 \]
Thus, the total number of plates shipped is \( \boxed{725} \).