Solve the Problem $A X = B$ , Which Can Be Solved to Determine the Price for Books

Solve the problem.
-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) .


Use this information to set up a matrix equation of the form $A X = B$ , which can be solved to determine the price for each type of sale book. Solve this matrix equation to find the price of a book with an orange 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) $\$ 5.44$
B) $\$ 5.08$
C) $\$ 5.33$
D) $\$ 5.91$