Indigo makes two separate investments, one paying  
6
  percent and the other paying  
8
  percent simple interest per year. She invests a total of  
$
7100
 , and her annual interest earnings are  
$
508
 . How much did she invest at each rate?

Let the amount Indigo invested at 6% be denoted as $ x $, and the amount invested at 8% be denoted as $ 7100 - x $ (since her total investment is $7100).

The total interest earned in one year is $508, and we know the formula for simple interest is:

\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]

Since the time is 1 year, we can simplify the formula to:

\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]

Now, set up two equations based on the two investments:

\[
\text{Interest from the 6% investment} = x \times 0.06
\]
\[
\text{Interest from the 8% investment} = (7100 - x) \times 0.08
\]

The total interest from both investments is $508, so:

\[
x \times 0.06 + (7100 - x) \times 0.08 = 508
\]

Now, solve this equation:

\[
0.06x + 0.08(7100 - x) = 508
\]
\[
0.06x + 568 - 0.08x = 508
\]
\[
-0.02x + 568 = 508
\]
\[
-0.02x = 508 - 568
\]
\[
-0.02x = -60
\]
\[
x = \frac{-60}{-0.02}
\]
\[
x = 3000
\]

So, Indigo invested $3000 at 6%. The remaining amount is:

\[
7100 - 3000 = 4100
\]

Thus, she invested $4100 at 8%.

### Summary:
- Indigo invested $3000 at 6%.
- She invested $4100 at 8%.

Would you like more details, or have any questions?

Here are 5 related questions:
1. What is the formula for simple interest?
2. How does compound interest differ from simple interest?
3. If Indigo had invested at 7% instead of 6%, how would her total earnings change?
4. What happens if she invests for multiple years under simple interest?
5. How would the solution change if the interest rates were swapped?

**Tip**: When solving for unknowns, organizing your equations clearly can help avoid errors and speed up the process.

Indigo makes two separate investments, one paying 6 percent and the other paying 8 percent simple interest per year. She invests a total of $7100, and her annual interest earnings are $508. How much did she invest at each rate?

Find out how to calculate the amounts invested at different interest rates to achieve a specific annual interest. This problem uses algebraic techniques and the simple interest formula, suitable for high school students in Grades 9-12.

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