Originally Posted by

**Jhevon** Ok, let's take this step by step:

Let $\displaystyle x$ be the amount of money invested in loans

Let $\displaystyle n$ be the amount of money invested in notes

Let $\displaystyle b$ be the amount of money invested in bonds

Since the company invests a total of $1 million, we have:

$\displaystyle x + n + b = 1$

Since the short-term loans pay annual interest at a rate of 10%, the treasury notes pay 8% interest, and the bonds pay 4% interest, and the total interest for the year is $0.06 million, we have:

$\displaystyle 0.1x + 0.08n + 0.04b = 0.06$

Since, the company has three times as much money invested in municipal bonds as in treasury notes, we have:

$\displaystyle b = 3n$

or

$\displaystyle b - 3n = 0$

Thus, we need to solve the system:

$\displaystyle \left( \begin{array}{ccc} 1 & 1 & 1 \\ 0.1 & 0.08 & 0.04 \\ 0 & -3 & 1 \end{array} \right) \left( \begin{array}{c} x \\ n \\ b \end{array} \right) = \left( \begin{array}{c} 1 \\ 0.06 \\ 0 \end{array} \right) $

Can you use this reasoning to set up the system for the second?