Specific Heat Capacity help G4.2 (a+b)

I am a bit stuck on this question for a while:
a) A certain quantity of ice requires 10.0 J to heat it to melting temperature. It then requires 100 J to melt it. Calculate the initial temperature of Ice.
- Calculated the mass using the 10J and the Latent heat of fusion which got me 2.895 x 10^-5 kg which I used to calculate the initial temperature which got me -1650 degrees celsius which doesn't seem right.

b) The water at the freezing point in part A is then heated using a further 100 J. What is the final temperature?
I need clarification on whether I need to add the energy to heat the Ice.

For part (a), I doubt you can use 10.0 J of energy to determine the mass of ice because there are 2 unknown quantities, namely the mass of ice and initial temperature.

Instead, you can use the 100 J to find the mass of ice because the product of the mass of ice and the specific latent heat of fusion of ice is equal to 100 J.

For part (b), there is no need to add energy to heat the ice because the ice has melted to turn into water at 0 °C.