Question

An amphitheater charges $74 for each seat in Section A, $59 for each seat in Section B, and $28 for lawn seat. There are three times as many seats in Section B as in Section A. The revenue from selling all 13,000 seats in $503,00. Let x be the number of seats in A, y be the number of seats in B, and z be the number of lawn seats. which system of equations represent the situation?


y=3x
x+y+z=13,000
74x+59y+28z=503,000


y=3x
74x+59y+28z=13,000
x+y+z=503,000

Answer 1

First, we know that y = 3x, because the problem stated that there are 3 times as many seats in section B, represented by y, as there are in section A, represented by x.

Second, we know that the total number of seats is 13,000. Since one seat is equal to x, y, or z (depending on the seating section), we can conclude that

x + y + z = 13000

Third, we know that the total profit of the amphitheater is $503,000. We know the profit of a section in the amphitheater is equal to the price of one seat multiplied by the number of seats in that section. Similarly, we know the price of any selected seats is equal to the price of one seat in a certain section multiplied by the number of seats. Represented as an equation, we find that the profit of Section A is 74x, the profit of Section B is 59y, and the profit of the lawn seats is 28z. Thus, the entire profit of the amphitheater is 74x + 59y + 28z = 503000.

Thus, our answer is the last set of equations:

y=3x

74x+59y+28z=13,000

x+y+z=503,000