Suppose a chunk of metal is immersed in boiling water (10degreesC), then is quickly transferred into a Styrofoam cup containing 250g of water at 20Celcius. After a minute or so, the temp of contents are 24Celcius. Assume no significant energy is transferred between the contents of the cup & surroundings. The heat cap. of cup is negligible.

Question

All I'm wondering for these are the equations I should use. I've written out how I would go about solving the problem, if you could tell me if I have the right idea that would be great.

a) How much heat is gained by the water?
b) How much is lost by the metal?

So for these two, I thought originally I would use the heat conduction equation? So, Q/t = kA (Th-Tc / L). Except now after typing it, I realize I don't have L. So now for a) I'm thinking Q = cmDeltaT..Would I sub in the water heat capacity for c, mass for m, and then the delta T as -4Celcius? And then Q would give me how much heat was gained by the water? Or lost by the metal?
For b), I'm thinking the same equation, but instead Q = CDeltaT, the Q would be the Q i got from a), the C would be the unknown, and Delta T would be the -4Celcius??

I'm really confused about this question Thank you for your help in advance