Question

Dante is holding a local dance for the community. He pays $125 to rent the local firehouse for the evening. He must also pay $3 for insurance for every guest at the party. If Dante charges $8 for the entry to the dance,how many tickets must he sell in order to recover all the money he has to pay

Answer 1

25 tickets

Explanation:

Let x = the number of guests

The fixed expense is $125 for the rental.

The variable expense is the insurance, which is $3 per guest.

For x number of guests, the insurance cost is 3x.

The total expense is the fixed expense plus the variable expense, or

3x + 125

The money he receives is a variable amount depending on the number of guests. He charges $8 per guest, so, for x number of guests, he will receive 8x amount of money.

To break even, the revenue and the expenses must be equal. Now we set the amount he receives equal to the amount he spends, and we solve for x, the number of guests.

8x = 3x + 125

Subtract 3x from both sides.

5x = 125

Divide both sides by 5.

x = 25

Answer: 25 tickets