What will be the final equilibrium temperature when \(100 \mathrm{~g}\) of water at \(30^{\circ} \mathrm{C}\) and \(200 \mathrm{~g}\) of water at \(80^{\circ} \mathrm{C}\) are mixed in an insulated container? \(\left(C_{P}\right.\) for water \(\left.=4185 \mathrm{~J} / \mathrm{kg}^{\circ} \mathrm{C}\right)\)

(a) \(45.4^{\circ} \mathrm{C}\)

(b) \(72.2^{\circ} \mathrm{C}\)

(c) \(63.3^{\circ} \mathrm{C}\)

(d) \(39.9^{\circ} \mathrm{C}\).