Answer :
There are 44 students total (in the group), so the number of oboe players, the number of clarinet players, and the number of flute players all add to 44.
b + c + f = 44
We know that there are 8 oboe players, so:
8 + c + f = 44
Subtract 8 from both sides
c + f = 36
There are half(1/2) as many people playing the clarinet as the flute. so however many people play the flute, there are half that number playing clarinet. We can say that the number of clarinet players = 1/2 * the number of flute players.
c = 1/2 * f
Plug 1/2 * f into the previous equation for c...
c + f = 36
1/2 * f + f = 36
Divide all the terms by 1/2, a.k.a. multiply by 2
f + 2f = 72
3f = 72
f = 24
So, there are 24 flute players. Plug that number back into one of our old equations:
c + f = 36
c + 24 = 36
c = 12
There are 8 oboe players, 12 clarinet players, and 24 flute players.
b + c + f = 44
We know that there are 8 oboe players, so:
8 + c + f = 44
Subtract 8 from both sides
c + f = 36
There are half(1/2) as many people playing the clarinet as the flute. so however many people play the flute, there are half that number playing clarinet. We can say that the number of clarinet players = 1/2 * the number of flute players.
c = 1/2 * f
Plug 1/2 * f into the previous equation for c...
c + f = 36
1/2 * f + f = 36
Divide all the terms by 1/2, a.k.a. multiply by 2
f + 2f = 72
3f = 72
f = 24
So, there are 24 flute players. Plug that number back into one of our old equations:
c + f = 36
c + 24 = 36
c = 12
There are 8 oboe players, 12 clarinet players, and 24 flute players.
