A person has a bag containing dimes and nickels. There are a total of 91 coins in the bag, and the total value of the coins is $\$ 6.80$. Determine how many dimes and nickels are in the bag. There are dimes. There are nickels. Submit Question

Step 1 ：Let's denote the number of dimes as x and the number of nickels as y. We know that a dime is worth 10 cents and a nickel is worth 5 cents.

Step 2 ：We can set up the following two equations based on the information given: \(x + y = 91\) (total number of coins) and \(10x + 5y = 680\) (total value of coins in cents).

Step 3 ：Solving this system of equations will give us the values of x and y.

Step 4 ：The solution to the system of equations is \(x = 45\) and \(y = 46\).

Step 5 ：So, the final answer is: There are \(\boxed{45}\) dimes and \(\boxed{46}\) nickels in the bag.