Question

question: 24
max takes 12 credits of classes at college a and 7 credits of classes at college b. dominique takes 5.5 credits of classes at college a and 13 credits of classes at college b. the cost of tuition is computed by multiplying the number of credits times the cost of each credit. the cost per credit at college a is $55, and the cost per credit at college b is $65. which of these shows the correct matrix product and calculation for the total tuition each student pays?
a.

b.

c.

d.

question: 25
the table shows the business activity for the month of december in a ski shop.

which matrix represents the rentals of skis and ski boots?
a.
c.
b.
d.

Explanation:

Question 24

Step1: Define the matrices

The student credit matrix (let's call it \( S \)) should have rows for each student (Max, Dominique) and columns for each college (College A, College B). So \( S =

$$\begin{bmatrix} 12 & 7 \\ 5.5 & 13 \end{bmatrix}$$

\). The cost per credit matrix (let's call it \( C \)) is a column matrix \(

$$\begin{bmatrix} 55 \\ 65 \end{bmatrix}$$

\) (since College A cost is 55, College B is 65, and we multiply credits by cost per credit).

Step2: Check matrix multiplication dimensions

For matrix multiplication \( S \times C \), the number of columns in \( S \) (2) must equal the number of rows in \( C \) (2), which it does. The resulting matrix will have rows equal to the number of rows in \( S \) (2, for Max and Dominique) and columns equal to the number of columns in \( C \) (1, total tuition).

Step3: Calculate for Max

Max's credits: 12 (College A), 7 (College B). Cost: \( 12 \times 55 + 7 \times 65 \). Calculate: \( 12\times55 = 660 \), \( 7\times65 = 455 \), sum: \( 660 + 455 = 1115 \).

Step4: Calculate for Dominique

Dominique's credits: 5.5 (College A), 13 (College B). Cost: \( 5.5 \times 55 + 13 \times 65 \). Calculate: \( 5.5\times55 = 302.5 \), \( 13\times65 = 845 \), sum: \( 302.5 + 845 = 1147.5 \).

Step5: Check the options

Now check the matrices in the options. Option C has the student credit matrix as \(

$$\begin{bmatrix} 12 & 7 \\ 5.5 & 13 \end{bmatrix}$$

\) and cost matrix \(

$$\begin{bmatrix} 55 \\ 65 \end{bmatrix}$$

\), and the calculations match (Max: 1115, Dominique: 1147.5).

We need the matrix for rentals of skis and ski boots, with sizes 6 - 10 and 11 - 14.

• Skis rentals: Size 6 - 10 is 11, Size 11 - 14 is 13.
• Ski Boots rentals: Size 6 - 10 is 21, Size 11 - 14 is 15.

So the matrix should have rows: Skis, Ski Boots; columns: Size 6 - 10, Size 11 - 14. So the matrix is \(

$$\begin{bmatrix} 11 & 13 \\ 21 & 15 \end{bmatrix}$$

\), which is Option A.

Answer:

C. \(

$$\begin{bmatrix} 12 & 7 \\ 5.5 & 13 \end{bmatrix}$$

$$\begin{bmatrix} 55 \\ 65 \end{bmatrix}$$

=

$$\begin{bmatrix} 1115.00 \\ 1147.50 \end{bmatrix}$$

\) (with Max and Dominique's totals as shown)

Question 25