Question: What is the advantage for rockets to [have multiple stages](http://en.wikipedia.org/wiki/Multistage_rocket)? 

Wouldn't a single stage with the same amount of fuel weigh less?

**Note** I would like a quantitative answer, if possible :-)

![alt text](https://i.stack.imgur.com/lswdV.jpg)

Answer: 
As Omega Centauri wrote, it is mainly about removing unused tank mass; for numbers, see Wikipedia article about [Ciołkowski's equation](http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation), especially the [example](http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation#Examples) there.
Launch weight would be lower if you had a fixed fuel load, and only one engine and fuel tank. However the specific impulse applied to the payload would be lower. The problem is that even when the fuel is say 90% exhausted, the rocket is still trying to accelerate the now grossly oversized fuel tank and engine. So the trick is to try to reduce the deadweight (structural mass) as the fuel is consumed. Another compromise system is to have jetisonable external fuel tanks, like the shuttle, which are thrown away once their fuel is consumed.