Jolene invest her savings in two bank accounts, one paying 3% and the other paying 11% simple interest per year. She puts twice as much in the lower yielding account because it is less risky. Her annual interest is $7089. How much did she invest at each rate?

To find out how much Jolene invested at each rate, we need to set up a system of equations based on the information given.

Let:
- $ x $ be the amount Jolene invested at 3%.
- $ y $ be the amount Jolene invested at 11%.

We know that:
1. Jolene invested twice as much in the 3% account as in the 11% account: $ x = 2y $.
2. The total interest earned from both accounts is $7089.

The interest earned from each account can be expressed as:
- Interest from the 3% account: $ 0.03x $
- Interest from the 11% account: $ 0.11y $

The total interest is:
\[ 0.03x + 0.11y = 7089 \]

Since $ x = 2y $, we can substitute $ x $ with $ 2y $ in the interest equation:
\[ 0.03(2y) + 0.11y = 7089 \]

Simplify the equation:
\[ 0.06y + 0.11y = 7089 \]
\[ 0.17y = 7089 \]

Now, solve for $ y $:
\[ y = \frac{7089}{0.17} \]
\[ y = 41700 \]

Now, find $ x $ using $ x = 2y $:
\[ x = 2 \times 41700 \]
\[ x = 83400 \]

So, Jolene invested:
- $ \$83,400 $ at 3%
- $ \$41,700 $ at 11%

Would you like a detailed explanation of each step or have any questions?

Here are 8 related questions for further exploration:
1. What would happen to Jolene's total interest if the interest rates were swapped?
2. How would the investment strategy change if the lower yielding account paid 4% instead of 3%?
3. What is the formula for calculating simple interest?
4. How much total interest would Jolene earn in 2 years with the same investment strategy?
5. If Jolene decided to invest equally in both accounts, how would that affect her total interest?
6. What is the total amount Jolene invested?
7. How can Jolene maximize her interest earnings while minimizing risk?
8. What are some other investment strategies that Jolene can consider?

**Tip:** Always check the feasibility and risk level of investment options before committing your savings to ensure they align with your financial goals.

Explore how Jolene invests her savings in two bank accounts, one paying 3% and the other 11% simple interest per year. Discover the solution to finding out how much she invested at each rate, along with detailed step-by-step calculations. Suitable for advanced high school students.

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