We have:
Specific heat capacity of water, Cw = 4.184 J/g.oC
Specific heat capacity of gold, Cg = 0.129 J/g.K
Specific heat capacity of silver, Cs = 0.233 J/g.K
Let T be the final temperature of the system.
We have, Heat lost by gold + heat lost by silver = heat gained by water.
Mathematically:
Substituting given values:
(let's ignore all units for now to solve for T):
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