Consider three identical metal spheres, A$,$ B$,$ and C$.$ Sphere A carries a charge of $+7q.$ Sphere B carries a charge of $-q.$ Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere $C$ is then touched to sphere A and separated from it$.$ Lastly, sphere $C$ is touched to sphere $B$ and separated from it$.($a$)$ What is the ratio of the final charge on sphere $C$ to $q?$ What is the ratio of the final total charge on the three spheres to $q(b)$ before they are allowed to touch each other and $($c$)$ after they have touched?