Question

Write a system of equations to solve the problem. A performer charges c(X) = 20x + 10,000, where x is the total number of attendees at a show. The venue charges $70 per ticket. After how many people buy tickets does the venue break even? people What is the value of the total tickets sold at that point?

Answer 1

Since the venue charges $70 per ticket, so for x tickets the venue will charge, R(x) = $70x

Now break-even point is that point where R(x) = C(x).

Now R(x) = C(x) implies,

70x = 20x + 10000

i.e. 70x - 20x = 10000

i.e. 50x = 10000

i.e. x = 10000/50

i.e. x = 200

.

Now at x = 200, we have,

R(x) = R(200) = (70×200) = 14000

C(x) = C(200) = (20×200) + 10000 = 4000 + 10000 = 14000

.

So the answers are,

200 people

$14000