Answer: 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
