Change CSS styling is post is in certain category

I’m working with a customized version of the main index page where individual posts each have their headline displayed in a box.

What I’d like to do is, if a certain post is under a specific category, the default CSS styles for the page would be overridden by new styles that, at the very least, change the box’s background color. I’d also like to be able to change the width of the box as well, if possible.

Any tricks to do this?