Use the worked example above to help you solve this problem. A $4\mathrm{.}75$ kg block of ice at $0$C is added to an insulated container partially filled with $10\mathrm{.}4$ kg of water at $15\mathrm{.}0$C$.$

$($a$)$ Find the final temperature, neglecting the heat capacity of the container.

$$C

$($b$)$ Find the mass of the ice that was melted.