A block of metal with a mass of $70\mathrm{.}3$ g is heated to $100$C and then dropped in a Styrofoam cup containing $50\mathrm{.}0$ g of water at $22\mathrm{.}5$C$.$ The final temperature of the block and water together is $32\mathrm{.}7$C$.$ What was the heat change of the water? What is the heat change of the metal? What is the specific heat of the metal?