Liquid water has a specific heat of 4.18 (joule)/(gram-degree). IT is constant well within 10% from 30 degrees to o degrees Centigrade. Ice (already at 0 degrees Centigrade) has heat fusion of 334 joules/gram. It's simpler to use calories to write the equation for melting x grams of ice in y grams of water:
(T1-T2) = (79.7 + T2)
Heat spent on the fusion of ice in water and the heating of water from melted ice is equal to the heat consumed from the cooling of the initial amount of water. The transfer of energy can be represented by:
C1mw(T1-T2)=C1mi(T2-Tmelt) + C2mi
Where C1 is the specific heat of water and C2 is the heat of fusion of water.