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

question 75

Multiple Choice

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 a red 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) \(\$ 6.50\)
• B) \(\$ 6.79\)
• C) \(\$ 6.87\)
• D) \(\$ 6.99\)

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Definitions:

Periodic Inventory System

An inventory accounting system where updates to inventory levels are made on a periodic basis, rather than continuously.

Perpetual Inventory System

An inventory management system where updates are made continuously as transactions occur, maintaining real-time inventory levels.

Journal Entries

The recordation of financial transactions in an accounting system.

After-tax Earnings

The net income a company generates after all taxes have been deducted from gross earnings.