Question

Problem: The table shows expressions to represent the number of 8th grade students

enrolled in different electives. The number of students enrolled in Art and Music is equal
to the number of students enrolled in Band and Journalism. Write and solve an equation.
Then find the number of students enrolled in each elective.
Class
Band
Art
Music
Journalism
What are you trying to find out:
Workspace:
# of Students
2n
7n+6
4n-2
2(4n+6)
Total
Solution:
I

Answer 1

So, the number of students in Band, Art, Music and Journalism are 2n, 7n+6, 4n-2 and 2(4n+6) respectively.

Since the number of students enrolled in Art and Music is equal to the number of students enrolled in Band and Journalism, we have the equation

7n + 6 + (4n-2) = 2n + 2(4n+6).

We now expand the brackets :
7n + 6 + 4n - 2 = 2n + 8n + 12
-> 11n + 4 = 10n + 12
-> 11n + 4 - 10n - 12 = 0
-> n - 8 = 0
-> n = 8.

Therefore, the number of students that enrolled in :
Band : 2n = 16 students.
Art : 7n + 6 = 62 students.
Music : 4n - 2 = 30 students.
Journalism : 8n + 12 = 76 students.

76 = 16 = 62 + 30 = 92, satisfying the requirement.