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The image shows a math problem involving simple interest. Here's a summary of the problem:

**Problem Statement:**
- Melissa has invested $8,200 in two accounts. One account pays 7% annual interest, and the other pays 8% annual interest.
- After one year, the total interest earned from both accounts is $609.

You need to determine how much money Melissa invested in each account. Let $ x $ represent the amount invested at 7%, and $ y $ represent the amount invested at 8%.

**Equations:**
1. $ x + y = 8200 $ (since the total amount invested is $8,200)
2. $ 0.07x + 0.08y = 609 $ (since the total interest earned is $609)

### To Solve:
You can use the substitution or elimination method to solve the system of equations.

Let's solve this step-by-step using substitution:

1. From the first equation:  
   $ y = 8200 - x $

2. Substitute $ y $ into the second equation:  
   $ 0.07x + 0.08(8200 - x) = 609 $

3. Distribute and combine like terms:  
   $ 0.07x + 656 - 0.08x = 609 $

   Simplifying:  
   $ -0.01x + 656 = 609 $

4. Isolate $ x $:  
   $ -0.01x = 609 - 656 $  
   $ -0.01x = -47 $  
   $ x = \frac{-47}{-0.01} = 4700 $

So, Melissa invested **$4,700** at 7%.

5. Substitute $ x = 4700 $ into $ y = 8200 - x $:  
   $ y = 8200 - 4700 = 3500 $

Melissa invested **$3,500** at 8%.

### Final Answer:
- **$4,700** was invested at 7%.
- **$3,500** was invested at 8%.

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:
1. How can you use the elimination method to solve the same system of equations?
2. What would the interest be if Melissa had invested the entire $8,200 at 7%?
3. What is the significance of the different interest rates in this problem?
4. How would the investment amounts change if the total interest earned was $700 instead of $609?
5. Can this type of problem be solved graphically? If so, how?

### Tip:
When dealing with percentage problems, always ensure that you convert percentages to their decimal forms before performing calculations.

Melissa invests $8,200 in two accounts paying 7% and 8% annual interest, respectively. After one year, the total interest earned is $609. How much was invested in each account?

Learn how to solve an investment problem involving simple interest and two different interest rates using systems of equations. Understand the step-by-step process to find the amounts invested at 7% and 8% interest rates. Suitable for students in Grades 8-10.

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