Problem

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.
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Final Answer: There are 32 quarters and 31 dimes in the bag.

Steps

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 32 quarters and 31 dimes in the bag.

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