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 th
ree 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?
<span>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</span>
