BTW, the usual answer to such a question is either "Nein, danke" or "Ja, bitte". Sometimes that is shortened to just "Danke" or "Bitte".
If you don't use it that way, the following happens: Once I saw that a rather small built foreign woman trying to carry a very heavy suitcase up a flight of stairs. So I asked her if she needed help. She said "Danke". I was confused, because it looked like she really had trouble with the suitcase, so I couldn't understand why she refused my offer. So I asked again. She again said "Danke". Finally it dawned on me that she was thanking me for the offer, and not refusing it. I was very close to just walking away after the first answer, because usually I don't pressure people into accepting help if they don't want it. That would probably have created a really awkward situation...
So, don't use "Danke" in that way :-) At least say "Ja, vielen Dank".