Twenty Twelve: how to change background on a per/page basis

I’m designing a website using a Twenty Twelve child theme. I have set the home page to Static and got it basically how I want it. However, I want some of the pages that are going to be menu items to have different backgrounds from the home page (and each other). I have not been able to figure out how to do this.

I got as far as using Firebug to identify one of these menu item pages, then adding the following CSS to my style sheet:

body.page-id-4 {
background-color: #FF0000 !important;
}

It didn’t work. The page retains the same background as the Static home page. (Note: I actually want to use a different background image, not colour, but thought I’d try to get the colour to change first – seems simpler).

There is a WP plugin that apparently assists in changing backgrounds on a per page/post basis, but I’d rather learn how to do it using CSS. I’m a beginner in this area, so am finding it daunting, but still want to persist until I get it right.

If anyone is able to assist, would be most appreciative.

Cheers
Ross