Write a system of equations to solve the problem
A performer charges C(x)=50x + 10,000, where x is the total number of attendees at a show. The venue charges $90.00 per ticket. After how many people buy tickets does the venue break even?
And what is the value of the total tickets sold?
Let's suppose that there are x attendees at the show who buy tickets.
The performer earns C(x) = 50x + 10,000 dollars from the concert.
The venue earns 90x dollars from ticket sales.
For the venue to break even, its earnings must be equal to the performer's earnings. Thus, we have:
50x + 10,000 = 90x
Solving for x:
40x = 10,000
x = 250
So after 250 people buy tickets, the venue breaks even.
To find the value of the total tickets sold, we simply substitute x = 250 into the equation for ticket sales:
Total ticket sales = 90x = 90(250) = 22,500 dollars.