What amount of hot water with a temperature of 80 ° C should be poured into cold water weighing 20 kg

What amount of hot water with a temperature of 80 ° C should be poured into cold water weighing 20 kg and a temperature of 10 ° C so that the temperature of the mixture is set to 30 ° C?

Quantity of heat:
Q = С * m * ∆t, С – specific heat capacity of water, m – mass of water, ∆t – change in water temperature (∆t = tн – tк, tн – initial temperature, tк – final temperature).
The amount of heat given off by hot water:
Q1 = С * m1 * (t1 – t3), t1 = 80 ° С, t3 = 30 ° С.
The amount of heat received by cold water:
Q2 = С * m2 * (t2 – t3), m2 = 20 kg, t2 = 20 ° С.
Q1 = Q2.
С * m1 * (t1 – t3) = С * m2 * (t2 – t3).
m1 = m2 * (t2 – t3) / (t1 – t3) = 20 * (10-30) / (80-30) = 8 kg.
Answer: You need to pour 8 kg of hot water.