Final temperature when 77g ice at 0°C mixes with 300g water at 50°C

[dmolson]

Determine the final temperature Tf, that results when 77 grams of ice at 0 °C are mixed with 300 grams of liquid water at 50 °C.
Specific heat of water: c = 1.00 cal/(gram*°C).
Heat of fusion for the ice - liquid water transition: cF = 79.7 cal/gram

I have tried this several times and several different ways and cannot solve the answer.

 

[OlderDan]

Determine the final temperature Tf, that results when 77 grams of ice at 0 °C are mixed with 300 grams of liquid water at 50 °C.
Specific heat of water: c = 1.00 cal/(gram*°C).
Heat of fusion for the ice - liquid water transition: cF = 79.7 cal/gram

I have tried this several times and several different ways and cannot solve the answer.

Tell us how you think it should be done, even if you did get the wrong answer. Then we can help you.

 

[QuantumCrash]

What are your thoughts on this?

Apply conservation of thermal energy. Take in the before and after situation and equate the increase of wnergy with the loss of energy.