Ice Cubes & Liquid Water - Thermodynamics

[ahaanomegas]

Homework Statement

Four ice cubes at exactly 0 \ { }^{\circ} \text{C} with a total mass of 53.5 \ \text{g} are combined with 115 \ \text{g} of water at 75 \ { }^{\circ} \text{C} in an insulated container. If no heat is lost to the surroundings, what will be the final temperature of the mixture?

Homework Equations

No specific formulas. Just basic thermodynamics, as explained in the solution.

The Attempt at a Solution

Magnitude of heat gained by Ice cubes = Magnitude of heat lost by Water
4m_{\text{one ice cube}}c_{\text{ice}}(T'-T_{\text{0-ice}})=m_{\text{water}}c_{\text{water}}(T_{\text{0-water}}-T')
From here, I used the numbers in my book and got the wrong answer [below]. :(

Spoiler

21 Degrees Celsius

 

[Borek]

You mean you end with water and ice at 21°C?

 

[ahaanomegas]

Yes, Sir, but that's my answer, not the correct one.

 

[Borek]

Sigh.

Have you ever seen ice at 21°C?

 

[ahaanomegas]

Ah! I guess I forgot the latent heat. That was obliviously silly. Thanks for helping me through my silliness! I'll re-try the problem once I can and, hopefully, I'll get it right this time around. :) Sorry and thank you, again.