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 = \(1 \text{ Cal/(g K)}\)

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