Step-by-step explanation:
Heat lost by the steam equals heat gained by the ice.
The steam first condenses, then cools. The amount of heat lost is:
q = x Lvapor + x C (100 − T)
q = 2254x + 4.18x (100 − T)
The ice first melts, then warms. The amount of heat gained is:
q = y Lfreeze + y C (T − 0)
q = 334y + 4.18y T
Setting the expressions equal:
2254x + 4.18x (100 − T) = 334y + 4.18y T
2254x + 418x − 4.184x T = 334y + 4.18y T
2672x − 334y = 4.18x T + 4.18y T
334 (8x − y) = 4.18 T (x + y)
T = 80 (8x − y) / (x + y)