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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?

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  1. 19 March, 14:23
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    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.
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