r - orchestra seats

m = main seats

b = balcony seats

1. r+m+b=500

2. 40r+30m + 20b=14400

3. 40r/2+30m + 20b=12400

subtract the 3rd from the 2nd:

40r/2=2000 => 20r=2000 => r =100

Now, from the 1st: m+b = 400 => b=400-m

substitute this and the value of r in the 2nd:

40*100+30m+20(400-m)=14400

or: 4000 + 30m+8000-20m=14400

10m=2400 =>m=240

b=400-m=160

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