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Let's define variables for the number of coins Ella has:

- Let **n** represent the number of nickels.
- Let **q** represent the number of quarters.

### Step 1: Set up the relationships based on the problem.

From the question:
- **q = n + 2** (There are 2 more quarters than nickels.)
  
Next, we know the total value of the coins is $2.00, or 200 cents:
- Each nickel is worth 5 cents, so the value of **n** nickels is **5n**.
- Each quarter is worth 25 cents, so the value of **q** quarters is **25q**.

Thus, the total value equation is:
\[ 5n + 25q = 200 \]

### Step 2: Substitute the expression for **q**.

Using the equation **q = n + 2**, substitute this into the total value equation:
\[
5n + 25(n + 2) = 200
\]

### Step 3: Simplify and solve.

Expand the equation:
\[
5n + 25n + 50 = 200
\]
\[
30n + 50 = 200
\]
Subtract 50 from both sides:
\[
30n = 150
\]
Solve for **n**:
\[
n = 5
\]

### Step 4: Find the number of quarters.

Since **q = n + 2**:
\[
q = 5 + 2 = 7
\]

### Conclusion:
- Ella has **5** nickels and **7** quarters.

Would you like more details on any step, or help with another problem?

Here are some related questions to consider:
1. What would happen if Ella had 3 more quarters than nickels?
2. How would the total value change if she had 10 quarters?
3. What if Ella only had dimes instead of nickels? How would the equation change?
4. Can you derive a general formula for any number of nickels and quarters given a total value?
5. How would this problem change if the total value were $3.00?

**Tip:** In word problems, always break down the relationships between variables before solving!

Ella has only quarters and nickels in her wallet. She has 2 more quarters than nickels. The total value of the coins is $2.00. How many of each coin does Ella have?

Learn how to solve a coin problem involving quarters and nickels. Ella has 2 more quarters than nickels, and the total value of the coins is $2.00. This solution covers algebraic concepts such as linear equations and substitution, suitable for students in Grades 6-8.

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