Respuesta :
ANSWER:
Regular gift basket = $19
Deluxe gift basket = $45
STEP-BY-STEP EXPLANATION:
We have the following:
x : cost of a regular gift basket
y : cost of a deluxe gift basket
With the data from the statement we create the augmented matrix:
[tex]\begin{pmatrix}19&2\\ \:\:0&1\end{pmatrix}\begin{pmatrix}x\\ \:y\end{pmatrix}=\begin{pmatrix}451\\ \:\:45\end{pmatrix}[/tex]We solve the matrix, like this:
[tex]\begin{gathered} \begin{pmatrix}19x+2y \\ 0\cdot\:x+1\cdot\:y\end{pmatrix}=\begin{pmatrix}19x+2y \\ y\end{pmatrix} \\ \\ \begin{pmatrix}19x+2y \\ y\end{pmatrix}=\begin{pmatrix}451 \\ 45\end{pmatrix} \\ \\ \begin{bmatrix}19x+2y=451\\ y=45\end{bmatrix} \\ \\ \begin{bmatrix}19x+2\cdot45=451\end{bmatrix}\rightarrow\begin{bmatrix}19x+90=451\end{bmatrix}\rightarrow\begin{bmatrix}19x=451-90\end{bmatrix}\rightarrow\begin{bmatrix}x=\frac{361}{19}\end{bmatrix}\rightarrow\begin{bmatrix}x=19\end{bmatrix} \\ \\ \begin{bmatrix}x=19 \\ y=45\end{bmatrix} \end{gathered}[/tex]Therefore,
The drama club is charging $19 for a regular gift basket and $45 for a deluxe gift basket.
