Answer:
Section A holds 25,000 seats, section B holds 14,500 seats and section C holds 10,500 seats.
Step-by-step explanation:
From the information given you can write the following equations:
A+B+C=50,000 (1)
28A+24B+20C=1,258,000 (2)
A=B+C (3)
A= number of seats in section A
B= number of seats in section B
C= number of seats in section C
You can replace (3) in (1) and (2) to get two equations:
B+C+B+C=50,000
2B+2C=50000
28(B+C)+24B+20C=1,258,000
28B+24B+28C+20C=1,258,000
52B+48C=1,258,000
The two equations are:
2B+2C=50000 (4)
52B+48C=1,258,000 (5)
You can isolate B in (4):
2B=50,000-2C
B=(50,000/2)-(2C/2)
B=25,000-C
Now, you can replace B in (5):
52(25,000-C)+48C=1,258,000
1,300,000-52C+48C=1,258,000
1,300,000-1,258,000=4C
42,000=4C
C=42,000/4
C=10,500
Now, you can replace the value of C in B=25,000-C:
B=25,000-10,500
B=14,500
Finally, you can replace the values of B and C in A=B+C to find A:
A=14,500+10,500
A=25,000
According to this, the answer is that section A holds 25,000 seats, section B holds 14,500 and section C holds 10,500.
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