You are mixing water with ice in an insulated container. The temperature of the ice is initially below its freezing point. The following are given:

the amount of heat absorbed by the ice if heated to its melting point: 6400 J,
the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 14,100 J,
the amount of heat given off by the water if cooled to its freezing point: 1800 J, and
the amount of heat given off by the water if it all freezes (which includes the heat needed to bring the water to its freezing point): 5200 J .
Based on this information, at equilibrium, which phases are present?

You are mixing water with ice in an insulated container. The temperature of the ice is initially below its freezing point. The following are given:

the amount of heat absorbed by the ice if heated to its melting point: 6400 ,
the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 14,100 ,
the amount of heat given off by the water if cooled to its freezing point: 1800 , and
the amount of heat given off by the water if it all freezes (which includes the heat needed to bring the water to its freezing point): 5200 .
Based on this information, at equilibrium, which phases are present?

ice only
water only
both ice and water

Since 6400J is more than 5200 J , as such the ice will nit completel melt. and also, the amount of heat released by water is not enough to melt the ice, it implies that the ice will still remain since 6400J > 5200J, therefore both ice and water will still remain at equilibrium.