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A stadium has 54,000 seats. Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,381,200 from each sold-out event. How many seats does each section hold?

a) 20,000 seats
b) 15,000 seats
c) 25,000 seats
d) 18,000 seats

User Rockit
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1 Answer

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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.

User Lufte
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