Keeping things together can raise a problem!

In a container of negigibe heat capacity, $200$ g of ice at $0^{\circ}C$ and $100$ g steam at $100^{\circ}C$ are added to $200$ g water that has temparture $55^{\circ}C$ . Assume no heat is lost to the surroundings and the pressure in the container is constant $1.0$ atm. Now if the final temprature of the system and the mass of total water present at this temprature can be represented as $A$ (in degree Celsius) and $B$ (in grams), find $A+B$ .

Details and assumptions

Latent heat of fusion for ice = $80 \text{ Cal/g}$ , Latent heat of vaporization for water = $540 \text{ Cal/g}$ and specific heat of water = $1 \text{ Cal/(g K)}$