How to save changed SimpleXML object back to file?

So, I have this code that searches for a particular node in my XML file, unsets an existing node and inserts a brand new child node with the correct data. Is there a way of getting this new data to save within the actual XML file with simpleXML? If not, is there another efficient method for doing this?

public function hint_insert() {

    foreach($this->hints as $key => $value) {

        $filename = $this->get_qid_filename($key);

        echo "$key - $filename - $value[0]<br>";

        //insert hint within right node using simplexml
        $xml = simplexml_load_file($filename);

        foreach ($xml->PrintQuestion as $PrintQuestion) {

            unset($xml->PrintQuestion->content->multichoice->feedback->hint->Passage);

            $xml->PrintQuestion->content->multichoice->feedback->hint->addChild('Passage', $value[0]);

            echo("<pre>" . print_r($PrintQuestion) . "</pre>");
            return;

        }

    }

}