If 7.20 kg of ice at -5.00°C is added to 12.0 kg of water at 30°C, compute the final temperature.

Answer 1

The sum of heats added is zero .
heat added to ice+heatadded to water=0
first assumption: assume all the ice melts, if there is a solution below zero, you know that can't be .
heating up ice+heat ice melting+heat ice water heating+heatoriginal water=0
7.20*Cice*(0-(-5)+ 7.30*Hf+7.30Cwater(Tf-0)+12*cwater*(Tf-30)=0

Now do the math, and solve for Tf. Look up the specific heats for ice and water, and the heat of fusion for water.