A Bookstore Is Having a Sale $A X = B$ , Which Can Be Solved to Determine the Price Each

question 141

Multiple Choice

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 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) $6.79
• B) $6.87
• C) $6.50
• D) $6.99

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Definitions:

Nature

The physical world and everything in it that is not made by human beings, including plants, animals, and landscapes.

Invisible Hand

A term coined by Adam Smith to describe the self-regulating nature of the marketplace, where individuals' pursuit of their own self-interest often leads to beneficial effects for the society as a whole.

Adam Smith

An 18th-century Scottish economist and philosopher, best known for his works "The Wealth of Nations," which is considered the foundation of modern economic theory.

Competitive Market

A market structure characterized by a large number of sellers and buyers, where no single entity can dictate prices, leading to efficient distribution of goods and services.