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19 March, 16:22

Hillary is planning an expensive surprise party. She is choosing between two venues. The banquet hall at Hotel A will cost $431 to rent the room and $38 per guest. The banquet hall at Hotel B will cost $747 to rent the room and $16 per guest. How many people does Hillary have to invite before the cost of having the party at Hotel B is less than the cost of having a party at Hotel A?

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  1. 19 March, 17:32
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    Answer: Hillary would have to invite 15 people before the cost of having the party at Hotel B is less than the cost of having a party at Hotel A

    Step-by-step explanation:

    Let x represent the number of guests that Hillary would invite.

    The banquet hall at Hotel A will cost $431 to rent the room and $38 per guest. This means that the total cost of hosting x guests at hotel A is

    38x + 431

    The banquet hall at Hotel B will cost $747 to rent the room and $16 per guest. This means that the total cost of hosting x guests at hotel B is

    16x + 747

    For the cost of having the party at Hotel B to be less than the cost of having a party at Hotel A, it means that

    16x + 747 < 38x + 431

    747 - 431 < 38x - 16x

    316 < 22x

    22x > 316

    x > 316/22

    x > 14.36
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