Q5. - Algebra 2

Question

BUSINESS For Exercise 4 and 5, use the table and the following information.

 The manager of the Best Bagel Shop keeps records of each type of Bagel sold each day at their two stores. Two days of sales are shown below.

5. Find the sum of the two days’ sales using matrix addition. 

Step-by-Step Solution

Answer

The Sum of two days’ sales is $\left[\begin{array}{cc}232& 134\\ 159& 200\\ 120& 159\\ 149& 103\end{array}\right]$

Step 1 - Consider the table.

Step 3 - Write the matrices.

The data in the table can be organized in two matrices. One being for Monday and other is for Tuesday. Each column of bothe matrices will represent Store ( East or West) that is each matrix will have 2 columns.

 The rows of the matrices will represent the type of Bagel (Sesame, Poppy, Blueberry, Plain) that is each matrix will have 4 rows.

 From the table, the matrices will be,

 For Monday,

$\left[\begin{array}{ccc}\text{Types of Bagel}\ddots \text{Store}& \text{East}& \text{West}\\ \text{Sesame}& 120& 65\\ \text{Poppy}& 80& 105\\ \text{Blueberry}& 64& 77\\ \text{Plain}& 75& 53\end{array}\right]=\left[\begin{array}{cc}120& 65\\ 80& 105\\ 64& 77\\ 75& 53\end{array}\right]$

For Tuesday,

$\left[\begin{array}{ccc}\text{Types of Bagel}\ddots \text{Store}& \text{East}& \text{West}\\ \text{Sesame}& 112& 69\\ \text{Poppy}& 79& 95\\ \text{Blueberry}& 56& 82\\ \text{Plain}& 74& 50\end{array}\right]=\left[\begin{array}{cc}112& 69\\ 79& 95\\ 56& 82\\ 74& 50\end{array}\right]$

Step 3 - Calculate the sum of the matrices.

Matrices can be added if they are of the same dimension.

 Here, both the matrices are of dimension $(4\times 2)$  that is both are of same dimension. 

 Then addition can be performed.

 Add the corresponding elements,

$\begin{array}{c}\left[\begin{array}{cc}120& 65\\ 80& 105\\ 64& 77\\ 75& 53\end{array}\right]+\left[\begin{array}{cc}112& 69\\ 79& 95\\ 56& 82\\ 74& 50\end{array}\right]=\left[\begin{array}{cc}120+112& 65+69\\ 80+79& 105+95\\ 64+56& 77+82\\ 75+74& 53+50\end{array}\right]\\ =\left[\begin{array}{cc}232& 134\\ 159& 200\\ 120& 159\\ 149& 103\end{array}\right]\end{array}$

Here, in the final matrix represents the two days’ sales of each type of Bagel in east and west stores, that is:

$\left[\begin{array}{ccc}\text{Types of Bagel}\ddots \text{Store}& \text{East}& \text{West}\\ \text{Sesame}& 232& 134\\ \text{Poppy}& 159& 200\\ \text{Blueberry}& 120& 159\\ \text{Plain}& 149& 103\end{array}\right]$

Step 4 - State the conclusion.

Therefore, the sum of two days’ sales is $\left[\begin{array}{cc}232& 134\\ 159& 200\\ 120& 159\\ 149& 103\end{array}\right]$