3x3 Linear equation

Question

At Edmonds Community College freshman need to take a 100 level Math and English plus optional Philosophy course.

In any quarter the college needs to make available 6 less English sections than Math sections.

In any quarter student demand for the optional Philosophy course is half as many sections as English sections.

Available classrooms limit the total sections of all three courses to 76

Given these constraints how many sections of each course should the college make available each quarter to meet demand?

Answer 1

E = M-6

P = E/2 = (M-6)/2

E+P+M = 76

(M-6) + (M-6)/2 + M = 76

2(M-6) + (M-6) + 2m = 152

2m-12 + m-6 + 2m = 152

5m - 18 = 152

5m = 170

m = 34

34 math

28 english

14 philosophy