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

Dante should sell 25 tickets in order to recover all money he paid.

Step-by-step explanation:

Let us assume Dante has to sell m tickets to recover all the money he pays.

Now, the amount paid to local firehouse = $125

The per person insurance costs = $ 3

So, the insurance of M guests cost = M x (The cost of insurance per person)

= M x ($3) = 3M

So, the cost of insurance of M guest = 3 M ... (1)

Also, The per person ticket costs = $ 8

So, the cost of M guests tickets = M x (The cost per person)

= M x ($8) = 8 M

So, the cost of tickets of M guest = 8 M ... (2)

Now, the total cost paid by Dante in organizing

= Amount paid to FIRE house + total Insurance cost of M people

= $125 + 3 M

And, the amount he receives after selling M tickets = 8 M

Now, for M tickets: The amount Spend = Amount Earned

⇒ 125 + 3 M = 8 M

or, 125 = 5 M

or, M = 125/5 = 25 ⇒M = 25

Hence, Dante should sell 25 tickets in order to recover all the money he has to pay.