A stadium has 45,000 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 $1,168,800 from each sold-out event. How many seats does each section hold?

Question

Mathematics

Anneliese

3 April, 10:09

A stadium has 45,000 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 $1,168,800 from each sold-out event. How many seats does each section hold?

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Madilyn Whitney · Answer 1

A + b + c = 45,000

30a + 24b + 18c = 1,168,800 reduces to 5a + 4b + 3c = 194,800

a = b + c

b + c + b + c = 45,000

2b + 2c = 45,000

b + c = 22500 < = = = this is A

c = 22500 - b

5a + 4b + 3c = 194,800

5 (22500) + 4b + 3 (22500 - b) = 194,800

112500 + 4b + 67500 - 3b = 194,800

b + 180,000 = 194,800

b = 194,800 - 180,000

b = 14,800 <===here is b

a = b + c

22500 = 14800 + c

22500 - 14800 = c

7700 = c < = = here is c

so ... A = 22,500, B = 14,800, and C = 7,700