Mojave art club is selling t shirts for a fundraiser. A local company charges $35 to set up the logo and $4.25 per t shirt if x t shirts are

Question

Mojave art club is selling t shirts for a fundraiser. A local company charges $35 to set up the logo and $4.25 per t shirt if x t shirts are printed by the business.

If the art club charged $10 per shirt how many shirts would need to be sold to cover their costs?

function C(x)=35+4.25x/x

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Verity 6 months 2021-08-24T13:01:42+00:00 1 Answers 0 views 0

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    2021-08-24T13:02:48+00:00

    Answer:

    At least 7 shirts would need to be sold to cover their costs

    Step-by-step explanation:

    Cost of producing x t-shirts.

    The cost of producing x t-shirts is a flat fee of 35 plus 4.25 per t-shirt. So

    C(x) = 35 + 4.25x

    Earnings of selling x t-shirts:

    Charges $10 per t-shirt, so it earns 10 for each t-shirt it sells.

    E(x) = 10x

    How many shirts would need to be sold to cover their costs?

    To cover the costs, we need that the earnings are equal or higher than the costs. So

    E(x) \geq C(x)

    10x \geq 35 + 4.25x

    5.75x \geq 35

    x \geq \frac{35}{5.75}

    x \geq 6.09

    Since we cannot sell a decimal part of a shirt, at least 7 shirts would need to be sold to cover their costs

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