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The problem asks about Phyllis's investment, which totals $23,000. Part of the money is invested at a 5% interest rate, and the remainder at 6%. After one year, she earned a total of $1,280 in interest. We need to determine how much she invested at each rate.

Let's define variables:
- Let $ x $ be the amount invested at 5%.
- Then, $ 23000 - x $ is the amount invested at 6%.

Using the formula for simple interest $ I = P \times r \times t $, where:
- $ P $ is the principal (amount invested),
- $ r $ is the interest rate (as a decimal),
- $ t $ is the time in years (1 year in this case),
the total interest can be expressed as follows:

\[
\text{Interest at 5%} = x \times 0.05
\]
\[
\text{Interest at 6%} = (23000 - x) \times 0.06
\]

The total interest is the sum of these two amounts, which equals $1,280:

\[
x \times 0.05 + (23000 - x) \times 0.06 = 1280
\]

Now, I'll solve this equation for $ x $, the amount invested at 5%.Phyllis invested $10,000 at a 5% interest rate and $13,000 at a 6% interest rate.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the total interest change if the interest rates were switched?
2. What if the total investment was $30,000 instead of $23,000, but the total interest earned remained $1,280?
3. How much would Phyllis have earned if she invested everything at 6%?
4. What would the total interest be after 2 years if the same rates and investments were maintained?
5. What is the difference in interest earned between the two portions?

**Tip**: Always check if your interest problem deals with simple interest or compound interest, as the formulas differ.

Phyllis invested $23,000, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After one year the total interest earned on these investments was $1,280. How much money did she invest at each rate?

Solve a real-world problem involving simple interest where Phyllis invests $23,000 with part at 5% and the remainder at 6%, earning $1,280 in total interest after one year. Learn the step-by-step process of using algebra to find how much was invested at each rate.

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