Respuesta :
Answer:
Math sections = 20
English sections = 16
Philosophy sections = 8
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of Math sections.
y is the number of English sections.
z is the number of Philosophy sections.
Available classrooms limit the total sections of all three courses to 44.
This means that [tex]x + y + z = 44[/tex]
4 less English sections than Math sections.
This means that [tex]y = x - 4[/tex]
In any quarter student demand for the optional Philosophy course is half as many sections as English sections.
This means that [tex]z = \frac{y}{2} = \frac{x - 4}{2}[/tex]
Finding the number of Math sections:
We have both y and z as functions of x. So
[tex]x + y + z = 44[/tex]
[tex]x + x - 4 + \frac{x-4}{2} = 44[/tex]
[tex]2x + \frac{x-4}{2} = 48[/tex]
Multiplying everything by 2
[tex]4x + x - 4 = 96[/tex]
[tex]5x = 100[/tex]
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20[/tex]
Then
[tex]y = x - 4 = 20 - 4 = 16[/tex]
[tex]z = \frac{y}{2} = \frac{16}{2} = 8[/tex]. So
Math sections = 20
English sections = 16
Philosophy sections = 8
