heat lost be warm metal + heat gained by water + heat gained by foam cup = 0
[mass warm metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccup x (Tfinal-Tinitial)]
Substitute and solve for specific heat metal.
Post your work if you get stuck.
A sample of unknown metal has a mass of 36.7 g. This metal was placed in boiling water at 96.0oC until the metal had reached the temperature of the water. The metal was then placed in a foam cup with 50.0 g of water in it at 20.0oC. The cup absorbs 42.0 J/oC, and the temperature of the water went up to 24.0oC. What is the specific heat of the metal?
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