Tickets to a dance cost $5.00 and the projected attendance is 350 people. It is further projected that for every $0.50 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $3,360?
A) $9.50
B) $11.00
C) $19.00
D) $12.00

Question

Quizplus · Accepted Answer

Let x be the number of $0.50 increases in ticket price.
The equation to represent the total receipts is:
Total receipts = (5 + 0.5x)(350 - 5x)

We need to solve for x in the equation below, where the total receipts equal $3,360:
3360 = (5 + 0.5x)(350 - 5x)

Expanding and simplifying the equation gives us:
0.5x^2 - 22.5x + 672 = 0

Using the quadratic formula, we can solve for x:
x = 23 or x = 14

Since we are looking for the ticket price, we need to plug in the value of x into (5 + 0.5x).
When x = 23, ticket price = $18.50, which is not a valid option.
When x = 14, ticket price = $12.00.

Therefore, the answer is D) $12.00.

Tickets to a Dance Cost $5