I disagree with @[B]DizMe[/B] .
You DO NOT have to pay for everything just because you invite someone on an expensive vacation with you. If you have plenty of money to burn, then knock yourself out. However, there is no RULE that says you have to pay for 100% and it is not RUDE when you're talking about spending hundreds to thousands of dollars on another child.
My DD is also a single child and we have taken friends with us multiple times. Each time I ask the parents to pay for something, usually passes or airfare plus spending money. We pay for the hotel (since it's the same with an extra kid) and food. Since I choose where we eat, I'm prepared to pay for what ever that costs. Sometimes we'll pay for airfare and sometimes park passes but never both. I talk to the parents first and float the idea and when I do I tell them what I am going to pay for and what I'd like them to pay for. I have never had a parent turn me down. It's a win-win. Their kid gets to go on vacation for a couple hundred dollars and my kid has company.