Chapter 3.6, Problem 12CYU

a.

To determine

To find: Matrix for the registration fees and Matrix for the number of students.

Answer to Problem 12CYU

Registration fees matrix is

  $\left[\begin{array}{ccc}165& 110& 239\end{array}\right]$

Number of student matrix is

  $\left[\begin{array}{cc}35& 28\\ 32& 17\\ 18& 12\end{array}\right]$

Explanation of Solution

Given equation:

Quinn’s Gym charges the following registration fees: class-by-class, $165;11-class pass, $110; unlimited pass, $239.

Table represents Number of students in Quinn’s Gym.

From the given table

We can write a matrix of number of students,

First rows represent the number of students of class-by-class pass and Second row represents the 11-class pass and Third row represents number of students of unlimited pass.

Columns represents the two types of students they are Aerobics students and Step Aerobics.

Therefore,

Number of columns will be 2

Therefore,

Number of student matrix is

  $\left[\begin{array}{cc}35& 28\\ 32& 17\\ 18& 12\end{array}\right]$

From given information

Quinn’s Gym charges the following registration fees: class-by-class, $165;11-class pass, $110; unlimited pass, $239.

First column represents the registration fees of class-by-class pass and Second column represents the registration fees for 11-class pass and Third column represents registration fees of unlimited pass.

There is only one row which represents the registration fee for each pass.

Therefore,

Registration fees matrix is

  $\left[\begin{array}{ccc}165& 110& 239\end{array}\right]$

b.

To determine

To find: Add the elements of each row and interpret the results.

Answer to Problem 12CYU

Total amount received by gym = $\$22955$

Explanation of Solution

Given equation:

Quinn’s Gym charges the following registration fees: class-by-class, $165;11-class pass, $110; unlimited pass, $239.

Table represents Number of students in Quinn’s Gym.

Number of student matrix is

  $\left[\begin{array}{cc}35& 28\\ 32& 17\\ 18& 12\end{array}\right]$

Registration fees matrix is

  $\left[\begin{array}{ccc}165& 110& 239\end{array}\right]$

Therefore

Total amount of money the gym received from aerobics and step-aerobic registrations is

  $\begin{array}{l}T=\left[\begin{array}{ccc}165& 110& 239\end{array}\right]\times \left[\begin{array}{cc}35& 28\\ 32& 17\\ 18& 12\end{array}\right]\\ \Rightarrow T=\left[\begin{array}{cc}\left(165\times 35\right)+\left(110\times 32\right)+\left(239\times 18\right)& \left(165\times 28\right)+\left(110\times 17\right)+\left(239\times 12\right)\end{array}\right]\\ \Rightarrow T=\left[\begin{array}{cc}5775+3520+4302& 4620+1870+2868\end{array}\right]\\ \Rightarrow T=\left[\begin{array}{cc}13597& 9358\end{array}\right]\end{array}$

Therefore, from above matrix we get

Amount of money gym received through Aerobics = $13597

Amount of money gym received through Step-Aerobics = $9358

Therefore,

Total Amount = Amount of money gym received through Aerobics + Amount of money gym received through Step-Aerobics.

  $\Rightarrow$ Total amount received by gym = $13597+9358$

  $\Rightarrow$ Total amount received by gym = $\$22955$