Question

A stadium has 52,000 seats. 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 $1,960,200 from each sold out event. How many seats does each section hold?

Answer 1

Let the number of seats in section A be x, that of section B y and that of secyion C z. Then
x + y + z = 52000 . . . (1)
x = y + z . . . (2)
42x + 36y + 30z = 1960200 . . . (3)

Putting (2) into (1), gives
2x = 52000
x = 52000/2 = 26000
From (2) and (3), we have
y + z = 26000 . . . (4)
42(26000) + 36y + 30z = 1960200
36y + 30z = 1960200 - 1092000
36y + 30z = 868200 . . . (5)

(4) * 30 => 30y + 30z = 780000 . . . (6)

(5) - (6) => 6y = 88200
y = 88200/6 = 14700

From (4), z = 26000 - 14700 = 11300

Therefore, there are 26,000 seats in section A, 14,700 seats in section B and 11,300 seats in section C.