To solve this, we simply equate the change in enthalpy for the two substances since heat gained by water is equal to heat lost of aluminum. We know that the heat capacity of aluminum is 0.089 J/g°C and that of water is 4.184 J/g°C. Therefore:
450.2 (95.2 - T) (0.089) = 60 (T – 10) (4.184)
3,814.45456 – 40.0678 T = 251.04 T – 2,510.4
291.1078 T = 6,324.85456
T = 21.7°C