A person has a bag containing quarters and dimes. There are a total of 63 coins in the bag, and the total value of the coins is $\$ 11.10$. Determine how many quarters and dimes are in the bag. There are quarters. There are dimes. Question Help: Message instructor Submit Question

Step 1 ：Let's denote the number of quarters as 'q' and the number of dimes as 'd'.

Step 2 ：From the problem, we can derive two equations: \(q + d = 63\) (since the total number of coins is 63) and \(0.25q + 0.10d = 11.10\) (since the total value of the coins is $11.10).

Step 3 ：Solving this system of equations gives us the values of 'q' and 'd'.

Step 4 ：The solution to the system of equations is {d: 31, q: 32}, which means there are 31 dimes and 32 quarters in the bag.

Step 5 ：Final Answer: There are \(\boxed{32}\) quarters and \(\boxed{31}\) dimes in the bag.