Equilibrium temperature of cold aluminum in warm water

[Brit412]

Homework Statement

A 150g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to -196 degrees C. The cylinder is immediately placed in an insulated cup containing 60.0g of water at 15.0 degrees C. What is the equilibrium temperature of the system?

Homework Equations

Q(water) = m(water) c(water) (∆T)
Q(water to ice)= m(water) Lfusion of ice
Q(aluminum) = m(aluminum) c(aluminum)(∆T)

The Attempt at a Solution

My problem is how to find the equilibrium temperature using those equations?

 

[Carid]

My preference would be to work in °Kelvin not °celsius. In which case...

HeatLost = HeatGained

HeatLost = MassWater*SpecificHeatWater*(InitialWaterTemp-FinalTemp) + MassWater*LatentHeat

HeatGained = MassAluminium*SpecificHeatAluminium*(FinalTemp-InitialAluminiumTemp)