Objects A and $B$ have the same mass of $4\mathrm{.}1$ kg and are at their melting points. They melt when $3\mathrm{.}0{10}^{4}J$ of heat is added to A and when $10{10}^{4}J$ is added to B $.($a$),($b$)$ Determine the latent heat of fusion for the substance from which each object is made. $($c$)$ Find the heat required to melt object A when its mass is $8\mathrm{.}2$ kg $.$

$($a$)L_{f,A}=$

$($b$)L_{f,B}=$

$($c$)Q=$