Answer
$\left(\begin{array}{c}a \\ a\end{array}\right) x_{1}\left[\begin{array}{c}110 \\ 4 \\ 20 \\ 2\end{array}\right]+x_{2}\left[\begin{array}{c}130 \\ 3 \\ 18 \\ 5\end{array}\right]=\left[\begin{array}{c}295 \\ 9 \\ 48 \\ 8\end{array}\right]$
(b) $x_{1}=1.5, x_{2}=1$
Work Step by Step
\[
\begin{array}{l}
110 x_{1}+130 x_{2}=295 \\
4 x_{1}+3 x_{2}=9 \\
20 x_{1}+18 x_{2}=48 \\
2 x_{1}+5 x_{2}=8
\end{array}
\]
Representation of data in equation. $\mathrm{x} 1$ is the number servings of Cheerios and $\mathrm{x} 2$ is the number of serving
of Natural Cereal.
\[
x_{1}\left[\begin{array}{c}
110 \\
4 \\
20 \\
2
\end{array}\right]+x_{2}\left[\begin{array}{c}
130 \\
3 \\
18 \\
5
\end{array}\right]=\left[\begin{array}{c}
295 \\
9 \\
48 \\
8
\end{array}\right]
\]
Representation of data in vector equation,
\[
\left[\begin{array}{ccc}
110 & 130 & 295 \\
4 & 3 & 9 \\
20 & 18 & 48 \\
2 & 5 & 8
\end{array}\right]
\]
Equivalent matrix equation of data.
\[
\left[\begin{array}{ccc}
110 & 130 & 295 \\
4 & 3 & 9 \\
20 & 18 & 48 \\
2 & 5 & 8
\end{array}\right] \sim\left[\begin{array}{ccc}
1 & 0 & 1.5 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}\right]
\]
Row reduce the matrix.
\[
x_{1}=1.5, x_{2}=1
\]
serving of cherrios with 1 serving of natural cereal requried to make desired mixture.
