Question

How much ice initially at -4 °C is needed to cool down 250 g of water at 80 °C to 0°C?
Take the specific heat capacity of ice to be 2060 J kg-1°C-1

Answer 1

ambiguous...

more ice...none of which melts

OR

less ice...all of which melts

OR

some ice...which partially melts

Answer 2

but they want exactly just enough.
Heat in = heat to raise ice to 0 from -4 (specific heat of ice * ice mass * 4) + heat to melt ice (heat of fusion of water * ice mass)
=
Heat out = specific heat water * 80 * mass of water