A teaching assistant performs an experiment using an aluminum cup that contains $225$ g of water and a $130$ g copper stirrer, all initially at $27\mathrm{.}0$C$.($Note that the student wears insulated gloves when handling the stirrer.$)$ The teaching assistant then adds a sample of silver to the water. The sample has a mass of $461$ g and is initially at a temperature of $86\mathrm{.}0$C$.$ After stirring the mixture until it reaches thermal equilibrium, the teaching assistant measures a final temperature of $32\mathrm{.}0$C$.$ What is the mass $($in g$)$ of the aluminum cup?