Use a Graphing Calculator and the Method of Matrix Inverses

Multiple Choice

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of books that are on sale. Each row of the table gives information about the numbers of book purchases and the total cost of the purchase (before taxes) .
$\begin{array}{c|c|c|c|r}\text { Person } & \text { Green } & \text { Red } & \text { Orange } & \text { Total Cost } \\\hline \text { Bob } & 1 & 2 & 2 & \$ 29.04 \\\text { Sue } & 1 & 3 & 2 & \$ 35.91 \\\text { Fred } & 1 & 2 & 3 & \$ 34.21\end{array}$

Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$ , which can be solved to determ: the price for each type of sale book. Solve this matrix equation to find the price of a book with an ori sticker.
Use the fact that for $A = \left[ \begin{array} { l l l } 1 & 2 & 2 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \\ - 1 & 1 & 0 \\ - 1 & 0 & 1 \end{array} \right]$ .

A) $\$ 5.17$
B) $\$ 5.64$
C) $\$ 4.81$
D) $\$ 5.06$