# Thread: Forming System of equations for matrices from a word problem

1. ## Forming System of equations for matrices from a word problem

19. An investment firm offers 3 stock portfolios: A, B and C. The number of blocks of each type of stock
in each of these portfolios is as follows:
Portfolio
A B C
High 6 1 3
Med 3 2 3
Low 1 5 3
Suppose a client wants 26 blocks of high-risk stock, 25 blocks of moderate-risk stocks, and 29 blocks
of low-risk stock. Determine the number of each portfolio that should be suggested to the client by
solving the appropriate system of equations.

my attempt:
I got a 1x3 Matrix with 3 variables x, y, z multiplied by the 3x3 matrix above, but when i try to solve i get a messed up answer.. any help is appreciated

2. Hello, s0urgrapes!

Must be your algebra . . . The answers come out nicely.

19. An investment firm offers 3 stock portfolios: A, B and C. The number
of blocks of each type of stock in each of these portfolios is as follows:

. . . . . $\text{Portfolio}$
$\begin{array}{c|ccc}
& A & B & C \\ \hline
\text{High} & 6 & 1 & 3 \\
\text{Med} & 3 & 2 & 3 \\
\text{Low} & 1 & 5 & 3 \end{array}$

Suppose a client wants 26 blocks of high-risk stock,
25 blocks of moderate-risk stocks, and 29 blocks of low-risk stock.

Determine the number of each portfolio that should be suggested
to the client by solving the appropriate system of equations.

We have: . $\begin{bmatrix} 6 & 1 & 3 \\ 3 & 2 & 3 \\ 1 & 5 & 3\end{bmatrix}\begin{bmatrix}A\\B\\C\end{bmatrix} \;=\;\begin{bmatrix}26\\25\\29\end{bmatrix} \qquad\Rightarrow\qquad \begin{bmatrix}A\\B\\C\end{bmatrix}\;=\;\begin{bma trix}1\\2\\6\end{bmatrix}$