Next time, a way to save some money on fluid would be use your process but instead of mixing new fluid with the old stuff use water. Water does not have the lubricity of fluid for the water pump but as long as you aren't running the engine that long it isn't going to hurt anything.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas