The student council is holding a dance for the school. The council pays $420 to rent a local firehouse for the evening. The council must also pay $2 per guest that attends for insurance. If the council charges $8 per ticket for the dance, how many tickets must they sell in order to recover all of the costs for the facility?

they need to sell 70 tickets in order to recover all of the costs for the facility.

Step-by-step explanation:

Let x represent the number of tickets that they will sell.

The council pays $420 to rent a local firehouse for the evening. The council must also pay $2 per guest that attends for insurance. This means that the total cost of admitting x guests would be

2x + 420

If the council charges $8 per ticket for the dance, then the revenue that would be generated from admitting x guests would be 8x.

The number of tickets they need to sell in order to recover all of the costs for the facility would be

8x = 2x + 420

8x - 2x = 420

6x = 420

x = 420/6

x = 70

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: