The system of equations representing the investment scenario is:
. 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:
![\[ \begin{cases} x + y + z = 12,000 \\ z = 4x \\ 0.04x + 0.065y + 0.08z = 832.50 \end{cases} \]](https://img.qammunity.org/2024/formulas/mathematics/college/gch6u8mh9lzuaws8x9x9fnhmzwh1kz2gd1.png)