Coolant

I was changing the coolant in my wifes Mercedes and in the manual it states that the engine plug should also be opened to let engine coolant out. Due to the position, I couldn't get to that plug, so I just emptied at the radiator, then filled with plain water, then ran the car and emptied at the radiator again (so some of that engine coolant has circulated and came out the radiator, leaving a more diluted solution left in the engine). The entire coolant system holds about 12 Qt and about 6 Qt comes out of the radiator. So after all this, I think I am now left with about 6 Qt of pretty much clear water & dilute solution in the engine. Now the manual indicates the mixture should be 50/50 water/coolant. So in order to get about 50/50 in the entire system, I assume I now need to add close to 6 Qt of 100% coolant (6 Qt water is already left in the engine, plus 6 Qt added pure coolant = 12 Qt total of 50/50 in the entire system). True??

I guess there is some Pantera related question here. When changing coolant on the Pantera, is a good portion also left in the engine as in the example above? If so, then adding 50/50 to a flushed system may not really give 50/50?? Somehow this feels like one of those trick math questions.