posted by kb .
When you take a bath, how many kilograms of hot water (48°C) must you mix with cold water (13°C) so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 185 kg. Ignore any heat flow between the water and its external surroundings.
Call mass hot water H.
Then mass cold water is 185-H.
H*specific heat water x (Tfinal-Tinitial) + (185-H)*specific heat water x (Tfinal-Tinitial) = 0
Solve for H and C.
Check my thinking. Post your work if you get stuck.