Q38. - Algebra 2

Question

For Exercises 36-39, use the following price list for one-day admissions to the community pool.

 

38. Write a matrix that represents the cost of admission before 6:00 P.M. and a matrix that represents the cost of admission after 6:00 P.M..

Step-by-Step Solution

Answer

The matrix representing the data for males and females are:

$\begin{array}{l}\text{ Before 6:00 P.M.}\\ A=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}3& 4.50\\ 4.50& 6.75\end{array}\right]\end{array}$and  $\begin{array}{l}\text{ After 6:00 P.M.}\\ B=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}2& 3.50\\ 3& 5.25\end{array}\right]\end{array}$

Step 1 - Define the concept of organizing data in matrix

A matrix is a rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets. Data is organized in such a way that each position has a purpose. Each value of the matrix is called an element.

Step 2 - Write the matrix depicting cost of admissions before 6:00 P.M

Let the first matrix representing the cost of admissions before 6:00 P.M be A. Then, 

$\begin{array}{l}\text{ Before 6:00 P.M.}\\ A=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}3& 4.50\\ 4.50& 6.75\end{array}\right]\end{array}$

Step 3 - Write the matrix depicting cost of admissions after 6:00 P.M

Let the matrix representing the cost of admissions after 6:00 P.M be B. Then,

$\begin{array}{l}\text{ After 6:00 P.M.}\\ B=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}2& 3.50\\ 3& 5.25\end{array}\right]\end{array}$