Matrix math problem solution

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 4 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 44

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

Answer 1

Philosophy is optional. What if no Philosophy?

E = M - 4 and E + M = 44

substituting: M - 4 + M = 44. Then M would be 24 and E would be 20.

If max. P: P = 0.5E = 0.5(M - 4) = 0.5M - 2

P + E + M = 44

(0.5M - 2) + (M - 4) + M = 44

2.5M = 50, then M = 20; E = 16; P = 8.

Looks like they'd have to reduce sections in E and M by 4 each to accommodate the P sections.

I guess the answer lies somewhere in between these limits?!!