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?

20°C

Explanation:

Heat gained by the colder water = heat lost by the warmer water

m₁ C (T − T₁) = m₂ C (T₂ − T)

m₁ (T − T₁) = m₂ (T₂ − T)

(500) (T − 10) = (100) (70 − T)

5 (T − 10) = 70 − T

5T − 50 = 70 − T

6T = 120

T = 20

The final temperature is 20°C.