Question

How do I solve this thank you.

Answer 1

The system of equations representing the investment scenario is:
`\[ \begin{cases} x + y + z = 12,000 \\ z = 4x \\ 0.04x + 0.065y + 0.08z = 832.50 \end{cases} \]`. Here, x, y, and z are the amounts invested in the 4%, 6.5%, and 8% funds, respectively.

Let's denote the amount invested in the fund paying 4% as x, the amount invested in the fund paying 6.5% as y, and the amount invested in the fund paying 8% as z.

The total sum invested is $12,000, so we have the equation:

x + y + z = 12,000

The amount invested in the fund paying 8% is four times the amount in the 4% fund, so:

z = 4x

The total annual interest from all three funds is $832.50, and the interest from each fund is calculated by multiplying the amount invested by the interest rate:

0.04x + 0.065y + 0.08z = 832.50

So, the system of equations is:

`\[ \begin{cases} x + y + z = 12,000 \\ z = 4x \\ 0.04x + 0.065y + 0.08z = 832.50 \end{cases} \]`