m = mass of metal
M = mass of water
c = specific heat
c of water = 1 cal/g *C
use the formula
Q = mcΔT = McΔT
(27g)*(c)*(107 C - 27.3 C) = (54.2g)*(1 cal/g *C)*(27.3 C - 22 C)
2152 * c = 287.26
c = specific heat of metal = .133 cal/g *C
1 cal / 4.186 j/g *C = .133 cal / x
= .557 J/g *C