https://file.aiquickdraw.com/mathbot/file/1727227888607juk0z602.jpeg

The problem you provided involves investing $38,000 in two different stocks: Stock Boll and Stock Coff. The question aims to maximize the annual interest earned based on the following information:

- Stock Boll earns a 6% annual interest.
- Stock Coff earns a 4% annual interest.
- The buying limit on Stock Coff is $14,400.
- At least two times as much money must be invested in Stock Boll compared to Stock Coff.

### Let’s define the variables:

- Let $ x $ represent the amount invested in Stock Coff.
- The amount invested in Stock Boll will be $ 2x $ because the condition states that the investment in Stock Boll is at least twice the amount in Stock Coff.

### Setting up the equation:

Since the total amount invested is $38,000:
\[
2x + x = 38,000 \quad \Rightarrow \quad 3x = 38,000
\]

Solving for $ x $:
\[
x = \frac{38,000}{3} \approx 12,666.67
\]

So, $ x \approx 12,666.67 $ should be invested in Stock Coff, and the remaining amount in Stock Boll:
\[
2x = 2 \times 12,666.67 = 25,333.33
\]

### Checking the conditions:
- You invest approximately $12,666.67 in Stock Coff, which is below the $14,400 limit.
- You invest twice as much, approximately $25,333.33, in Stock Boll.

### Annual interest calculation:

1. The interest from Stock Boll (6% on $25,333.33):
\[
0.06 \times 25,333.33 = 1,520
\]

2. The interest from Stock Coff (4% on $12,666.67):
\[
0.04 \times 12,666.67 = 506.67
\]

### Total annual interest:
\[
1,520 + 506.67 = 2,026.67
\]

### Conclusion:
- You will earn a total annual interest of $2,026.67.
- Invest approximately $25,333.33 in Stock Boll and $12,666.67 in Stock Coff.

Let me know if you need further details or calculations! Here are some related questions:

1. What if the interest rates for both stocks were switched?
2. How would the solution change if the limit on Stock Coff was removed?
3. What happens if you want to invest equally in both stocks?
4. How would the interest differ if Stock Boll earned a higher rate than 6%?
5. What if you wanted to invest a different total amount, like $50,000?

**Tip**: When dealing with investment problems, setting up constraints clearly is crucial for solving the problem systematically.

You have $38,000 you would like to invest in two different stocks: Stock Boll and Stock Coff. The buying limit on Stock Coff is $14,400, and you want to spend at least two times as much money on Stock Boll as Stock Coff. If Stock Boll earns 6% annual interest and Stock Coff earns 4% annual interest, how much money (in dollars) should you invest in each stock to maximize your annual interest earned? What is the maximum annual interest (in dollars)?

Learn how to optimize an investment of $38,000 between Stock Boll (6% interest) and Stock Coff (4% interest) while adhering to the buying limit on Stock Coff. This problem explores linear equations, interest calculations, and strategies to maximize annual earnings.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation