Find the equilibrium temperature & the amount of ice/water

[jpastones]

Homework Statement

In an insulated vessel, 600g of ice at -20C is added to 250g of water at 18C.
Cice= 0.5 cal/gC, Cwater= 1 cal/gC. Lfusion= 80 cal/g.
Find the equilibrium temp of the system. Explain the reasons.
At the equilibrium temp, will the system be all water, all ice, or a mixture of both? Give the amounts of water and/or ice in the system at equilibrium.

Relevant Equations

Q=m*c*(Tf-Ti)
Q=m*Lfusion

Qsystem=0
Qsystem= Qice + Qwater
m*c*(Tf-Ti)ice + m*c*(Tf-Ti)water = 0

That's how far I've gotten and now I'm stuck!

 

[Orodruin]

A very important part of the question is "Explain the reasons." In your attempt you have not done that and so following your solution is a bit of guesswork. For example, when you write
$$
m_{\rm ice} c_{\rm ice}\Delta T_{\rm ice} + m_{\rm water} c_{\rm water} \Delta T_{\rm water} = 0
$$
(do not forget the subscripts!), what is your reasoning behind this?

Also, in the future, do not post images of your work. Type it out! As per forum policy.

 

[Chestermiller]

The three possibilities at the final state are: (1) all liquid water above 0 C (2) all ice below 0 C or (3) a combination of liquid water and ice at 0 C. What do you think your calculation has shown so far?