cart_controller.rb

respond_to :html, :json
 
def update
    @cart = Cart.find(params[:id])
    @cart.update_attributes(params[:cart])
    respond_with @cart 
end

show.html.erb

<script>
$(document).ready(function() {
	$('input[type=checkbox]').change(function() {
		$('#cart').fadeOut('fast', function() {

			$.ajax({
				url: '<%= update_store_cart_path %>',
				dataType: 'jsonp',
				type: 'PUT',	
				data: $('form').serialize(),
                                success: function(cart) {
                                   $('#cart').fadeOut().html('');
                                   cart.items.each(function(c,item) {
                                       $('#cart').append('<li>'+item.manufacturer+' '+item.model+'</li>');
                                   }
                                   $('#cart').fadeIn();
                                }
			});
		});
	});
});
</script>