Kristina invests a total of $9,000 in two accounts paying 3% and 6% simple interest, respectively. How much was invested in each account if, after one year, the total interest was $420.00.

A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use as your variable to represent the amount of money invested in the account paying 3% simple interest.
Equation:

B) The answers are:
$ was invested at 3% and
$ was invested at 6%.

Let's start by setting up the equation.

### A) Setting Up the Equation
Let $ x $ represent the amount of money invested in the account paying 3% simple interest. Therefore, the amount invested in the account paying 6% simple interest would be $ 9000 - x $.

The interest earned from the account paying 3% interest is $ 0.03x $, and the interest earned from the account paying 6% interest is $ 0.06(9000 - x) $.

Since the total interest after one year is $420, we can set up the equation as follows:

\[
0.03x + 0.06(9000 - x) = 420
\]

### B) Solving the Equation
Now, let's solve the equation to find out how much was invested in each account.

\[
0.03x + 0.06(9000 - x) = 420
\]

Expanding the equation:

\[
0.03x + 540 - 0.06x = 420
\]

Combine like terms:

\[
-0.03x + 540 = 420
\]

Subtract 540 from both sides:

\[
-0.03x = 420 - 540
\]

\[
-0.03x = -120
\]

Divide both sides by -0.03:

\[
x = \frac{-120}{-0.03} = 4000
\]

So, $4,000 was invested at 3%.

Now, subtract $ x $ from $9,000 to find the amount invested at 6%:

\[
9000 - 4000 = 5000
\]

So, $5,000 was invested at 6%.

### Final Answers:
- **$4,000** was invested at 3%.
- **$5,000** was invested at 6%.

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

Here are 5 related questions to consider:
1. How would the problem change if the total interest after one year was $450?
2. What if the interest rates were 4% and 5% instead of 3% and 6%?
3. How much total interest would Kristina earn in two years under the same conditions?
4. What is the effect of changing the total amount invested from $9,000 to $10,000?
5. How would the solution change if the interest was compounded annually instead of being simple interest?

**Tip:** When solving investment problems, setting up the correct equation is crucial. Always double-check your variables and make sure they represent the correct amounts.

Learn how to calculate investments with simple interest. Kristina invests $9,000 in accounts with 3% and 6% interest rates. After one year, the total interest is $420. Follow a step-by-step solution to determine the amounts invested in each account.

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