An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $30 for each lawn seat. There are three times as many seats in Section B as in Section A. The revenue from selling all 23,000 seats is $870,000. How many seats are in each section of the amphitheater?

Question

Mathematics

Yin

11 November, 06:05

An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $30 for each lawn seat. There are three times as many seats in Section B as in Section A. The revenue from selling all 23,000 seats is $870,000. How many seats are in each section of the amphitheater?

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Nehemiah Hendrix · Answer 1

Section A seats = 1500 Section B seats = 4500 Lawn seats = 17000 Let's write a few equations to express what we know. A = number of seats in section A B = number of seats in section B L = number of law seats "There are three times as many seats in Section B as in Section A" B = 3A "all 23,000 seats" L = 23000 - A - B L = 23000 - A - 3A "The revenue from selling all 23,000 seats is $870,000" 870000 = 30L + 55B + 75A Now let's substitute 3A for B 870000 = 30L + 55 (3A) + 75A And substitute (23000 - A - 3A) = (23000 - 4A) for L 870000 = 30 (23000 - 4A) + 55 (3A) + 75A And solve for A 870000 = 30 (23000 - 4A) + 55 (3A) + 75A 870000 = 690000 - 120A + 165A + 75A 870000 = 690000 + 120A 180000 = 120A 1500 = A So we know that section A has 1500 seats. Because of B = 3A = 3*1500 = 4500, section B has 4500 seats. Finally, L = 23000 - A - B = 23000 - 1500 - 4500 = 17000 seats