Final answer:
To solve this problem, we can set up a system of equations using the information provided. By substituting the value of A into the second equation and simplifying, we can find the values of B and C. The number of seats in Section B is 18,000, and the number of seats in Section C is 9,000.
Step-by-step explanation:
To solve this problem, let's assign variables to each section: A for Section A, B for Section B, and C for Section C.
According to the problem, the number of seats in Section A equals the total number of seats in Sections B and C. So, we can write the equation: A = B + C.
We also know that the total number of seats in the stadium is 54,000, so we can write another equation: A + B + C = 54,000.
Finally, we know the prices of the seats in each section: Section A ($30), Section B ($24), and Section C ($18).
Using these equations, we can solve for the number of seats in each section:
We have the following system of equations:
A = B + C
A + B + C = 54,000
We can substitute the first equation into the second equation:
B + C + B + C = 54,000
2B + 2C = 54,000
Simplifying, we have:
B + C = 27,000
Since we know A = B + C, we can substitute this into the equation:
A = 27,000
Therefore, we have:
A = 27,000, B = ?, C = ?
Since we know the total number of seats in the stadium is 54,000, we can substitute the values into the equation:
27,000 + B + C = 54,000
B + C = 27,000
Now we have a system of two equations:
A = 27,000
B + C = 27,000
We can solve the system of equations to find the values of B and C.
The answer is: B = 18,000, C = 9,000.