Jyn Erso had $2000 in credits to invest. She chose to invest some in The Separatist Bank at 2.5% simple interest and some in the Republic Bank at 5% simple interest. At the end of the year she found that she had earned $55 in interest.
Knowing this, how much did she initially invest in each bank?


Let's solve this problem by letting:

- $ x $ be the amount Jyn invested in The Separatist Bank at 2.5% interest.
- $ 2000 - x $ be the amount Jyn invested in the Republic Bank at 5% interest.

### Step 1: Set up the interest equations

The total interest earned at the end of the year is given by the simple interest formula:
\[
I = P \times r \times t
\]
where:
- $ I $ is the interest,
- $ P $ is the principal (initial investment),
- $ r $ is the interest rate (as a decimal),
- $ t $ is the time in years (1 year in this case).

#### Interest from The Separatist Bank:
\[
\text{Interest from Separatist Bank} = x \times 0.025 \times 1 = 0.025x
\]

#### Interest from the Republic Bank:
\[
\text{Interest from Republic Bank} = (2000 - x) \times 0.05 \times 1 = 0.05(2000 - x) = 100 - 0.05x
\]

### Step 2: Total interest equation
We know that the total interest earned is $55, so:
\[
0.025x + (100 - 0.05x) = 55
\]

### Step 3: Solve for $ x $
Simplify the equation:
\[
0.025x + 100 - 0.05x = 55
\]
\[
-0.025x + 100 = 55
\]
\[
-0.025x = 55 - 100
\]
\[
-0.025x = -45
\]
\[
x = \frac{-45}{-0.025}
\]
\[
x = 1800
\]

So, Jyn invested **$1800** in The Separatist Bank.

### Step 4: Find the investment in the Republic Bank
The remaining amount she invested in the Republic Bank is:
\[
2000 - 1800 = 200
\]

### Final Answer:
- Jyn invested **$1800** in The Separatist Bank.
- Jyn invested **$200** in the Republic Bank.

Would you like more details on any part of this solution?

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Here are 5 questions that build on this concept:

1. What if Jyn invested the entire $2000 in the Republic Bank at 5%? How much interest would she have earned?
2. How would the problem change if the interest rates were compounded annually instead of using simple interest?
3. If Jyn had $3000 instead of $2000 to invest, how would the investment amounts change?
4. What is the total interest Jyn would earn after 2 years under the same conditions?
5. How much more interest would Jyn earn if she had invested the $2000 entirely in the Separatist Bank at 2.5% for 3 years?

**Tip:** When dealing with simple interest problems, remember that time is always a key factor. Make sure to adjust the time period accurately when solving for different durations.

Jyn Erso had $2000 in credits to invest. She chose to invest some in The Separatist Bank at 2.5% simple interest and some in the Republic Bank at 5% simple interest. At the end of the year she found that she had earned $55 in interest. Knowing this, how much did she initially invest in each bank?

Discover how to solve this simple interest problem involving Jyn Erso's $2000 investment. She splits her funds between The Separatist Bank at 2.5% interest and the Republic Bank at 5% interest, earning $55 in total. Follow the step-by-step algebraic solution to find how much was invested in each bank. Ideal for students in Grades 9-11.

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