250 people joined the community band.

Question

250 people joined the community band. Some intended to play a woodwind instrument,
some a brass instrument, and the others percussion. If 2 times as many people were
planning to play a woodwind instrument as a brass instrument, and if 70 fewer were
going to play percussion than a brass instrument, how many people were planning to
play each type of instrument?

Answer 1

Let

W = people playing woodwinds

B = people playing brass

P = people playing percussion

 

Total = W+B+P = 250

 

W = 2B since twice as many people were going to play a woodwind over brass

P = B-70 since 70 fewer people were going to play percussion than brass

 

If we substitute we get

T = W+B+P

250 = 2B + B + (B-70)

250 = 4B-70

 

Now you can solve for B and then solve for P and W