Add ajax-cart.php to functions.php, add cart.php to the theme's template where it is required.
<?php
<a class="cart-contents basket" href="<?php echo wc_get_cart_url(); ?>" title="<?php _e( 'View your shopping cart' ); ?>">
<span class="hidden-xs"><?php echo sprintf ( _n( '%d item', '%d items', WC()->cart->get_cart_contents_count() ), WC()->cart->get_cart_contents_count() ); ?> - </span>
<span class="basket-total"><?php echo WC()->cart->get_cart_total(); ?></span>
</a>
<?php
// AJAX update cart totals
add_filter( 'woocommerce_add_to_cart_fragments', 'woocommerce_header_add_to_cart_fragment' );
function woocommerce_header_add_to_cart_fragment( $fragments ) {
ob_start();
?>
<a class="cart-contents" href="<?php echo wc_get_cart_url(); ?>" title="<?php _e( 'View your shopping cart' ); ?>"><span class="hidden-xs"><?php echo sprintf (_n( '%d item', '%d items', WC()->cart->get_cart_contents_count() ), WC()->cart->get_cart_contents_count() ); ?> - </span><?php echo WC()->cart->get_cart_total(); ?></a>
<?php
$fragments['a.cart-contents'] = ob_get_clean();
return $fragments;
}