Answer:
There are 1000 seats in Section A, 5000 seats in section B and 6000 seats in Section C.
Step-by-step explanation:
Let the number of seats in Section A=x
Let the number of seats in Section B=y
Let the number of seats in Section C=z
The number of seats in section C equals the number of seats in sections A and B combined.
z=x+y......(I)
The arena holds 12,000.
x+y+z=12000......(II)
For a basketball game seats in Section A cost $100, seats in section B cost $50 and seats in section C cost $35.
Total revenue from ticket sales is $560,000
100x+50y+35z=560000.....(III)
The system of equation is given as:
z=x+y......(I)
x+y+z=12000......(II)
100x+50y+35z=560000.....(III)
Substitute z=x+y From (I) into Equation (II)
x+y+x+y=12000
2x+2y=12000
x+y=6000......(IV)
Substitute z=x+y From (I) into (III).
100x+50y+35(x+y)=560000
100x+35x+50y+35y=560000
135x+85y=560000.....(V)
From (IV), x=6000-y
135(6000-y)+85y=560000
810000-135y+85y=560000
50y=250000
y=5000
Recall From (IV), x=6000-y
x= 6000-5000=1000
From (I)
z=x+y=1000+5000=6000
There are 1000 seats in Section A, 5000 seats in section B and 6000 seats in Section C.
