[lbk]

I really need help on this question.  I can't just do the M₁C₁DT = M₂C₂DT equation, because I don't know how the enthalpy of fusion fits in.  The answer in the back of the book is 10.4 degrees celsius but I don't know how to get there.  Thanks in advance for your *delete me*

Suppose an ice cube weighing 36.0g at a temperature of -10.0 degrees celsius is placed in 360 g of water at a temperature of 20 degrees celsius.  Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings.  The enthalpy of fusion of ice is (DH_fus)   6.007 kJ/mol.  The molar heat capacity (c_p) of ice is 38 J K^- mol^- and c_p of water is 75 J K^- mol^-. 

[enahs]

I actually get 10.9, using the numbers provided.

You are just using q₁+q₁+q₃...=0 (where typically you just have two terms, and you can do this because you are assuming no heat is lost).

m₁*C_p1*(x-Ti)₁ + m₂*C_p2*(x-Ti)₂ + m*DH_fus = 0
Solve for x.