SOLUTION: Tickets to a school dance cost $5.00, and the projected attendance is 300 people. For every $0.50 increase in the ticket price, the dance committee projects that attendance will de

Question 390123: Tickets to a school dance cost $5.00, and the projected attendance is 300 people. For every $0.50 increase in the ticket price, the dance committee projects that attendance will decrease by 20. What ticket price will generate $1562.50 in revenue?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Tickets to a school dance cost $5.00, and the projected attendance is 300 people. For every $0.50 increase in the ticket price, the dance committee projects that attendance will decrease by 20. What ticket price will generate $1562.50 in revenue?
:
Let x = no. of .50 increases
Let x = no. of 20 people decreases
:
(5 + .5x)(300 - 20x) = 1562.50
FOIL
1500 - 100x + 150x - 10x^2 = 1562.5
A quadratic equation
-10x^2 + 50x + 1500 - 1562.5 = 0
:
-10x^2 + 50x - 62.5 = 0
Solve this using the quadratic formula

a=-10; b=50; c=-62.5

x =
x = 2.5
:
Ticket price: 2.5(.5) + 5.00 = $6.25
:
No. of ticket: 300 - 2.5(20) = 250 people
:
Revenue: $6.25 * 250 = $1562.5

RELATED QUESTIONS
Tickets to a school dance cost $4 and the projected attendance is 300 people. For every... (answered by ikleyn,josmiceli,ankor@dixie-net.com)

SOLVE FULLY. DEFINE VARIABLES, CREATE QUADRATIC EQUATION AND ANSWER PROBLEM. Tickets to... (answered by ankor@dixie-net.com)

Tickets to the school dance cost $4, and the projected attendance is 300 people. It is... (answered by ankor@dixie-net.com)

Tickets to a school dance cost $4, and the projected attendance is 300 persons. It is... (answered by ankor@dixie-net.com)

Tickets to a school dance cost $3, and the projected attendance is 325 persons. It is... (answered by lwsshak3)

When tickets at a dance cost $4, the expected attendance is 300 people. for every $0.10... (answered by Edwin McCravy)

A group on tour has been drawing crowds of 500 people. It is projected that for every $1... (answered by user_dude2008)

You're part of a high school committee whose purpose is to organize an upcoming school... (answered by stanbon)

When tickets for a rock concert cost $12, the average attendance was 500 people.... (answered by TimothyLamb)