Chapter 4.3, Problem 97SR

(a)

To determine

To Find: The matrix that represent the amount sold for each of the class and a matrix that shows the amount of money that the school earns for the each item sold.

Answer to Problem 97SR

The required matrix are $\left[\begin{array}{cc}72& 49\\ 68& 63\\ 90& 56\\ 86& 62\end{array}\right]$ and $\left[\begin{array}{c}1.00\\ 0.50\end{array}\right]$ .

Explanation of Solution

Given:

The given data is shown in Table 1

Table 1

Class	Wrapping Paper	Cards
Freshmen	72	49
Sophomores	68	63
Juniors	90	56
Seniors	86	62

The school gets $\$1.00$ for each roll of the wrapping paper that is sold $\$0.50$ for each of the box of car is sold.

Calculation:

The form from the given table is,

  $\left[\begin{array}{cc}72& 49\\ 68& 63\\ 90& 56\\ 86& 62\end{array}\right]$

The next set of matrix is,

  $\left[\begin{array}{c}1.00\\ 0.50\end{array}\right]$

(b)

To determine

To Find: The matrix that shows the amount that each of the class earns.

Answer to Problem 97SR

The required matrix is $\left[\begin{array}{c}96.50\\ 99.50\\ 118\\ 117\end{array}\right]$ .

Explanation of Solution

Obtain the number of class as,

  $\begin{array}{c}\left[\begin{array}{cc}72& 49\\ 68& 63\\ 90& 56\\ 86& 62\end{array}\right]\left[\begin{array}{c}1.00\\ 0.50\end{array}\right]=\left[\begin{array}{c}72\left(1\right)+49\left(0.5\right)\\ 68\left(1\right)+63\left(0.5\right)\\ 90\left(1\right)+56\left(0.5\right)\\ 86\left(1\right)+62\left(0.5\right)\end{array}\right]\\ =\left[\begin{array}{c}96.50\\ 99.50\\ 118\\ 117\end{array}\right]\end{array}$

(c)

To determine

To Find: The class that earns the most money.

Answer to Problem 97SR

The amount that the junior earns is $\$118$ .

Explanation of Solution

Consider the matrix is $\left[\begin{array}{c}96.50\\ 99.50\\ 118\\ 117\end{array}\right]$ .

The matrix shows that the amount that the junior earns is $\$118$ .

(d)

To determine

To Find: The amount of money that the school made from the fund raiser.

Answer to Problem 97SR

The school made the total amount of $431$ dollars from the fundraiser.

Explanation of Solution

The total amount made by the school is,

  $96+50+99.50+118+117=431$