carts_controller.rb

  def update_store_cart
    store = Store.find(params[:store_id])
    params[:item_ids] ||= []
    
    params[:item_ids].each do |i|
      Cart.add(current_user.id, i)
    end
    
    current_user.items.each do |i|
      Cart.drop(current_user.id, i.id) unless params[:item_ids].include?(i.id.to_s) || i.store != store
    end
    
        flash[:success] = "Your cart has been updated!"
    respond_to do |format|
      format.html {
        redirect_to (store_path(params[:store_id]))
      }
      format.js
    end
  end

show.html.erb

<script>
$(document).ready(function() {
	$('input[type=checkbox]').change(function() {
			$.ajax({
				url: '<%= update_store_cart_path %>',
				type: 'PUT',
				data: $('form').serialize(),
				success: function(cart, status, xhr) {
				}
		});
	});
});
</script>