Heat transfer calculation problem

[KurtWagner]

I must be doing something wrong here but I cannot figure out what it is1. Homework Statement
An insulated beaker with negligible mass contains a mass of 0.350kg of water at a temperature of 70.1∘C.
How many kilograms of ice at a temperature of − 11.6∘C must be dropped in the water to make the final temperature of the system 25.0∘C?

Take the specific heat for water to be 4190J/(kg⋅K) , the specific heat for ice to be 2100J/(kg⋅K) , and the heat of fusion for water to be 334kJ/kg .

Homework Equations

Q = mcT
Q = mcT + L_fm

The Attempt at a Solution

So basically I was just doing...

m_wc_w ΔT_w = m_i [(c_i ΔT_i) + L_{f i}]

which gives
ΔT_w = 70.1∘C. - 25∘C = 45.1K
ΔT_i = − 11.6∘C - 25∘C = 36.6K

0.350kg * 4190J/(kg⋅K) * (45.1K) = m_i [(2100J/(kg⋅K)*(36.6K)] +334kJ/kg]
66139.15J = 257140J/kg * m_i
m_i = 0.161kg

which does not turn out to be the right answer (I do not have access to the right answer).
Can anyone tell me what mistake I am making.
Any help would be greatly appreciated.

 

[SteamKing]

What happens to the ice when it reaches a temperature of 0 C? Is your equation equating the heat lost by the water in the beaker to the heat gained by the ice dropped into the beaker correct? You should first write out what happens to the ice after it is dropped into the beaker without applying any numbers.

 

[KurtWagner]

Q = mi [(ci ΔTi) + Lf i]

Would this equation not mean that each kilo of ice absorbs the heat needed to change its state and also to change its temp?
for each kilo 2100 Joules per degree change in temp but also the 334kJ to change its state?

Am i right in assuming that each kilo of ice changes through -11.6∘C to 0∘C, taking 24360J , changing state for 334000J, then continuing to change from 0∘C to 25∘C taking a further 52500J. Total = 410860J/kg

Whoops, that's different from above, but It is what I used in my calculations

 

[KurtWagner]

oh... It becomes water and has a different specific heat after 0∘C... hmmmm. Ill try that

 

[KurtWagner]

That worked.

Q_water = Q_ice + Q_icewater