Questions: Need help? Click here to learn! A nursery has 500,000 cf of pumpkin plants that need to be moved in a (single) type of tree? dogwood trees what is the smallest amount you can invest in the 4% and 4.1% with interest (there is more risk in the 4.1% fund) Your goal is to obtain a total annual interest income of 500 from the investments. Solve this problem using the following steps: 1. Let x = the amount invested at 4% and y = the amount invested at 4.1% 2. Write an equation for the total amount invested: x + y = ? 3. Write an equation for the total annual interest: 0.04x + 0.041y = 500 4. Solve this system of equations 5. The question has several parts that must be completed sequentially. If you stop at any part of the question, you will not receive any points for this step.

Solution Steps

To solve this problem, we need to determine the amounts to invest at two different interest rates to achieve a specific annual interest income. We will set up a system of linear equations based on the given conditions. The first equation will represent the total amount invested, and the second equation will represent the total annual interest. We will then solve this system of equations to find the values of \( x \) and \( y \).

1. Define \( x \) as the amount invested at 4% and \( y \) as the amount invested at 4.1%.
2. Write the equation for the total amount invested: \( x + y = \text{total amount} \).
3. Write the equation for the total annual interest: \( 0.04x + 0.041y = 500 \).
4. Solve the system of equations to find \( x \) and \( y \).

Let \( x \) be the amount invested at 4% and \( y \) be the amount invested at 4.1%.

We have the following equations based on the problem statement:

1. Total amount invested: \[ x + y = 500000 \]
2. Total annual interest: \[ 0.04x + 0.041y = 500 \]

Upon solving the system of equations, we find: \[ x = 20000000.0000000 \] \[ y = -19500000.0000000 \]

The solution indicates that \( x \) is an impractically large investment, while \( y \) is negative, which is not feasible in this context. This suggests that the total amount invested of \( 500,000 \) is insufficient to generate the desired interest income of \( 500 \) with the given interest rates.

Final Answer