mixing ice and water

[anasofia]

When determining the final temperature of mixing ice and water, given the amount and temperature of ice (in grams) and the amount and temperature of the water, how do you combine the q for melting the ice which I believe is g of ice * molar mass * molar heat capacity, and I know that mcat cold = mcat hot, but how does the q of fusion/melting of the ice combine with the q of bringing the ice and water to Tfinal, is the final equation just "q-fusion + qcold = qhot"

[MarissaSmith1B]

I do these types of problems in a series of steps rather than combining them into one equation. This just helps me make sure I get all my signs right.
1. Energy to change temperature
2. Energy of fusion

[Isabelle Huerta 2I]

In order to be able to determine the final temp of ice mixed with water, you have to combine heat absorbed from melting ice (q = m_ice * ∆H_fus) and heat absorbed from warming the ice and water (q = mC∆T). We have to find the total heat absorbed by the ice and the total heat released by the water when we are finding equilibrium (q_fusion + q_cold = q_hot).