You add 500 mL of water at 10°C to 100 mL of water at 70°C. What is the most likely final temperature of the mixture?
Would it not be the weighted average of the two temperatures....?
Suppose we knew of heat capacities (and we don't here because you have not quoted any). In a problem like this would we not expect that the final temperature is the WEIGHTED average of the two temperatures, according to the mass of each volume?
Anyway, you should check your text for a more sophisticated approach. But note that this calculation is quite amenable to a simple experiment, given a couple of beakers or polystyrene cups, and a thermometer. What did you find in the experiment?