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?

Question

Mathematics

Athena Small

3 June, 21:01

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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Answers (1)

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Scarlett Watkins · Answer 1

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