A stadium has 53,000. Seats sell for $ 42 in Section A, $ 36 in Section B, and $ 30 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 $ 1,996,800 from each sold-out event. How many seats does each section hold

Question

09-11-2017
Mathematics

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A stadium has 53,000. Seats sell for $ 42 in Section A, $ 36 in Section B, and $ 30 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 $ 1,996,800 from each sold-out event. How many seats does each section hold

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choixongdong choixongdong · Answer 1 · 2017-11-09T22:05:37+01:00

A = B + C = 53,000 / 2 = 26,500

section A: 26,500 (seats) x 42 = $1,113,000
$1,996,800 - $1,113,000 = $883,800

So now
B + C = 26,500 so B = 26,500 - C
36B + 30C = $883,800

substitute B = 26,500 - C into 36B + 30C = $883,800

36B + 30C = $883,800
36(26,500 - C) + 30C = $883,800
954,000 - 36C + 30C = $883,800
-6C = -70,200
C =11,700

B = 26,500 - C
B = 26,500 - 11,700
B = 14,800

Answer
A: 26,500 seats
B: 14,800 seats
C: 11,700 seats