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?

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Mathematics

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19 March, 16:31

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?

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Deven Blanchard · Answer 1

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