https://file.aiquickdraw.com/mathbot/file/1726443673475mup0bzmm.jpg

The problem is about determining the correct system of equations based on the given information:

- Jeremy has a total of $25 in dimes and nickels.
- Jeremy has 4 more dimes than nickels.

Let:
- $ d $ represent the number of dimes.
- $ n $ represent the number of nickels.

### Formulating the System of Equations:
1. **Total value equation**:
   - The value of a dime is $0.10 and the value of a nickel is $0.05. The total amount is $25.
   - This leads to the equation:
   \[
   0.10d + 0.05n = 25
   \]
   To simplify, multiply the entire equation by 100 to eliminate decimals:
   \[
   10d + 5n = 2500
   \]

2. **Relationship between dimes and nickels**:
   - Jeremy has 4 more dimes than nickels, which gives us the equation:
   \[
   d = n + 4
   \]
   This can also be written as:
   \[
   d - n = 4
   \]

### Now, let's compare the options provided in the image:

- **Option A**: 
   \[
   10d + 5n = 2500 \quad \text{and} \quad d - n = 4
   \]
   This system matches our equations exactly.

- **Option B** and **Option C** are incorrect because they have incorrect coefficients or the wrong structure in the equations.

- **Option D** switches the order in the second equation, but the form $ d - n = 4 $ is more standard.

### Conclusion:
The correct system of equations is **Option A**.

Would you like further explanation, or do you have any questions?

Here are 5 related questions to think about:
1. How do you convert the total value equation when the problem involves money?
2. What happens if Jeremy had 5 fewer dimes than nickels instead?
3. How would the system of equations change if the total amount were $30 instead of $25?
4. Can you solve the system of equations manually? What values of $ d $ and $ n $ do you get?
5. How can you generalize this type of problem for any number of dimes and nickels?

**Tip**: Always simplify equations by removing decimals, especially in money-related problems, to make the calculations easier.

Jeremy has a total of $25 in dimes and nickels. He has 4 more dimes than nickels. Which system of equations can be used to determine the number of dimes, d, and the number of nickels, n, that Jeremy has?

Learn how to solve a system of equations to determine the number of dimes and nickels Jeremy has, given their total value is $25, and he has 4 more dimes than nickels. Suitable for Grades 7-9 students.

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