Calorimetry in a totally insulating coffee cup?

Question

A sample of Al (specific heat = 0.900-J/g°C) weighing 222.5-g is boiled in water at sea level until it reaches 100.0°C.
The sample is dumped into a coffee cup containing an unknown mass of water that had reached equilibrium temperature 20.3°C.
The temperature of the water and Al rose to 37.5°C.
Assuming that no heat is absorded by the coffee cup, what was the mass of the water in the coffee cup. (in grams)

Answer 1

Please use ALGEBRA!
Water specific heat or heat capacity: 4.182 J/g°C
Al specific heat: 0.900 J/g°C
Let the mass of water in the coffee cup Calorimeter be X grams.
(222.5g)*(0.900 J/g°C)*(100.0°C - 37.5°C) = (X g)*(4.182 J/g°C)*(37.5°C - 20.3°C)
X = (222.5*0.900*62.5)/(4.182*17.2)
= 174 (grams)