analysing the reactions taking place will aid your understanding of redox and precipitate chemistry but the reactions is not essential.
the essential part is linking the mass of precipitate to the mass of silver in the coin. silver chloride is AgCl
there are two ways to find the mass of an element in a compound when the compound's formula and mass are known.
1) find amount in mole of compound and use subscript to find amount in mole of element, then use molar mass of element to find mass of element. eg. in this example, n(Ag)= n(AgCl) and m(Ag)= n(Ag).M(Ag)
2) use percentage composition shortcut (recommended for speed but more error- prone): m(Ag)= [M(Ag)/M(AgCl)].m(AgCl). i.e the fraction is the proportion of AgCl that is Ag by mass.
once you have found m(Ag), find the percentage composition using the relevant formula.