# Math Help - Matrix..

1. ## Matrix..

Hi There;

A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
A 7 88 1
B 6 90 1
C 10 70 2

How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?

2. Originally Posted by eureka
Hi There;

A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
A 7 88 1
B 6 90 1
C 10 70 2

How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?
Let a, b and c denote the number of bags of each grain required then
we have:

7a + 6b + 10c = 71 ..protien equation

88a + 90b + 70c = 854 ..carb. equation

a + b + 2c = 12 ..sodium equation.

These constitute a set of simultaneous linear equations which you should
solve.

RonL

3. Hello, eureka!

A rancher has to mix three types of feed for her cattle.
The following analysis shows the amounts per bag of grain:

$\begin{array}{ccccc} \text{Grain} & \text{Protein} & \text{Carb.} & \text{Sodium}\\ \hline \\
A & 7 & 88 & 1 & \\
B & 6 & 90 & 1 \\
C & 10 & 70 & 2\\ \hline \\
\text{Req.} & 71 & 854 & 12 \end{array}$

How many bags of each type of grain should she mix to provide
the requirements for protein, carbohydrates, and sodium?

Captain Black is absolutely correct.

The system of equation is: . $\begin{array}{ccc}7a + 6b + 10c \\ 88a + 40b + 70c \\ a + b + 2c\end{array}
\begin{array}{ccc}= \\ = \\ = \end{array}
\begin{array}{ccc}72 \\ 854 \\ 12\end{array}$

You said "matrix", so this is your quest . . .

Solve: . $\begin{pmatrix}7 & 6 & 10 & | & 71 \\ 88 & 40 & 70 & | & 854 \\ 1 & 1 & 2 & | & 12\end{pmatrix}$