How do you do this problem?

Question

A 30.5 g sample of an alloy at 93.2°C is placed into 47.0 g water at 21.6°C in an insulated coffee cup with a heat capacity of 9.2 J/K. If the final temperature of the system is 31.1°C, what is the specific heat capacity of the alloy?

I know about the q=mc delta T equation. I've tried using the equation, but I need something more apparently. There is some difference between heat capacity and specific heat capacity and I can't figure out how to use the heat capacity in the equation to solve the problem.

Answer 1

Please use algebra!
Let the specific heat capacity of the alloy to be X J/gK.
Heat released from this alloy: (30.5g)*(X J/gK)*(93.2°C-31.1°C), where K and C can be canceled (can you see why?).
Heat absorbed by the coffee cup: (9.2 J/K)*(31.1°C - 21.6°C).
Heat absorbed by water: (47.0 g)*(4.182 J/gK)*(31.1°C - 21.6°C).
Hence we have:
30.5*X*(93.2 -31.1) = (9.2 + 47.0*4.182)*(31.1 - 21.6)
You do the math.