Question

two hundred fifty grams of iron is heated from 27 degree Celsius to 300 degree Celsius . how much ice can be melted and raised to a temperature of 27 degree Celsius by hot iron?

Answer 1

Figure the heat in the iron.

250*spchatFe*(300-27)

now the tricky part: the ice and water.
heat to melt ice+water
m*Lf + m*cwater*(27-0). This assumes the initial temperature of the ice was 0C.

set the two heats equal, and solve for mass ice/water m.