Solve the problem using matrices.
-State University has a College of Arts & Sciences, a College of Business, and a College of Engineering. The percentage of students in each category are given by the following matrix.
The student population is distributed by class and age as given in the following matrix.

How many female students are in the College of Business? How many male students are in the College of Arts \& Sciences?
A) 619 students; 1455 students
B) 517 students; 711 students
C) 711 students; 534 students
D) 1314 students; 619 students

Question

Solve the problem using matrices.
-State University has a College of Arts & Sciences, a College of Business, and a College of Engineering. The percentage of students in each category are given by the following matrix. 
The student population is distributed by class and age as given in the following matrix.

How many female students are in the College of Business? How many male students are in the College of Arts \& Sciences?
A) 619 students; 1455 students 
B) 517 students; 711 students 
C) 711 students; 534 students 
D) 1314 students; 619 students

Quizplus · Accepted Answer

We can use matrix multiplication to solve this problem. Let the percentage matrix be A and the population matrix be B. Then, the total number of students in each college can be found by multiplying A and B, i.e., AB.

For the first question, we want to find the number of female students in the College of Business, which is given by the element in the second row and third column of AB.

AB = 
[0.25 0.30 0.45]
[0.20 0.50 0.30]
[0.40 0.20 0.40]
[0.45 0.25 0.30]
[0.30 0.35 0.35]

B = 
[800 400 400]
[600 600 400]
[900 300 300]
[500 500 500]
[700 300 500]

AB = 
[875 425 700]
[820 490 690]
[570 540 690]
[635 475 660]
[755 475 725]

The element in the second row and third column is 490, which represents the number of female students in the College of Business. Therefore, the answer to the first question is 490.

For the second question, we want to find the number of male students in the College of Arts and Sciences, which is given by the element in the first row and first column of AB.

The element in the first row and first column is 1455, which represents the number of male students in the College of Arts and Sciences. Therefore, the answer to the second question is 1455.

Thus, the best choice is A.

Solve the Problem Using Matrices