Kevin and Randy Muise have a jar containing 53 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $9.65. How many of each type of coin do they have?

Let's define two variables for the number of each type of coin:

- Let $ q $ be the number of quarters.
- Let $ n $ be the number of nickels.

We are given two key pieces of information:
1. The total number of coins is 53, so:
   \[
   q + n = 53
   \]
2. The total value of the coins is $9.65, or 965 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, we can write the value equation as:
   \[
   25q + 5n = 965
   \]

### Step 1: Simplify the second equation
We can divide the second equation by 5 to simplify:
\[
5q + n = 193
\]

### Step 2: Solve the system of equations
Now, we have the system:
1. $ q + n = 53 $
2. $ 5q + n = 193 $

We can subtract the first equation from the second equation to eliminate $ n $:
\[
(5q + n) - (q + n) = 193 - 53
\]
\[
4q = 140
\]
\[
q = 35
\]

### Step 3: Solve for $ n $
Now that we know $ q = 35 $, substitute this into the first equation to find $ n $:
\[
35 + n = 53
\]
\[
n = 18
\]

### Conclusion
Kevin and Randy Muise have 35 quarters and 18 nickels.

Would you like more details on any part of this solution?

Here are 5 related questions:
1. How can you verify the solution by calculating the total value of coins?
2. How would the problem change if the total number of coins was 60 instead of 53?
3. What if the total value of the coins was $11.25 instead of $9.65?
4. How can you solve this problem using substitution instead of elimination?
5. How would this problem change if there were three types of coins instead of two?

**Tip**: When solving systems of equations, choosing the right method (substitution or elimination) can simplify your work significantly.

Discover how to solve a system of linear equations to find out how many quarters and nickels are in a jar containing 53 coins with a total value of $9.65. This problem illustrates key algebra concepts and is suitable for students in Grades 6-8.

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