Add the current page slug to your body class. Very handy!

gistfile1.php

<?php
add_filter('body_class', function($classes) {
    global $wpdb, $post;
    if (is_page()) {
        if ($post->post_parent) {
            $parent  = end(get_post_ancestors($current_page_id));
        } else {
            $parent = $post->ID;
        }
        $post_data = get_post($parent, ARRAY_A);
        $classes[] = 'parent-' . $post_data['post_name'];
        $classes[] = $post->post_name;
    }
    return $classes;
});