Final answer:
To solve the problem, we can set up a system of equations based on the given information. By solving the system of equations, we can find the number of quarters and dimes.
Step-by-step explanation:
Let's solve this problem using a system of equations.
Let's assume that the number of quarters is x. Since there are 34 more dimes than quarters, the number of dimes would be x+34.
The value of the quarters can be represented as 0.25x, and the value of the dimes would be 0.10(x+34).
According to the problem, the total value of the coins is $19.85. So we have the equation:
0.25x + 0.10(x+34) = 19.85
Solving this equation, we get x = 31. So there are 31 quarters and 31+34=65 dimes.