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

question 351

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 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) \(\$ 5.91\)

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Definitions:

Population Mean

The average of a set of characteristics or values within an entire population.

Midrange

The statistical measure calculated by adding the highest and lowest values in a dataset and then dividing by two, indicating the midpoint of the data range.

Variance

A measure of the dispersion or spread of a set of data points around their mean value, indicating how much the data points differ from the average.

Standard Deviation

A calculation that quantifies the extent of deviation or spread within a group of data points.