Company A charges $32 per person to host a banquet. Company B charges an initial fee of $30 and charges $30 per person. At what number of pe

Question

Company A charges $32 per person to host a banquet. Company B charges an initial fee of $30 and charges $30 per person. At what number of people will Company B be the cheaper option?

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Diễm Thu 4 years 2021-08-14T18:44:36+00:00 1 Answers 6 views 0

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  1. Tryphena
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    2021-08-14T18:46:26+00:00
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    Answer:

    At 16 people company B will be the cheaper option

    Step-by-step explanation:

    Assume that the number of people is x

    ∵ Company A charges $32 per person to host a banquet

    ∵ The number of people is x

    ∴ The cost of company A = 32x

    ∵ Company B charges an initial fee of $30 and charges $30 per person

    ∵ The number of people is x

    ∴ The cost of company B = 30x + 30

    ∵ Company B be is the cheaper option

    → That means the cost of company B < The cost of company A

    ∴ 30x + 30 < 32x

    → Subtract 30x from both sides

    ∵ 30x – 30x + 30 < 32x – 30x

    ∴ 30 < 2x

    → Divide both sides by 2

    ∴ 15 < x

    → 15 smaller than x means x is greater than 15

    ∴ x > 15

    → To make company B cheaper, the number of people should be > 15

    ∵ The first integer greater than 15 is 16

    ∴ At 16 people company B will be the cheaper option

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