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
[tex]C(x) = 35 + 4.25x[/tex]
Earnings of selling x t-shirts:
Charges $10 per t-shirt, so it earns 10 for each t-shirt it sells.
[tex]E(x) = 10x[/tex]
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
[tex]E(x) \geq C(x)[/tex]
[tex]10x \geq 35 + 4.25x[/tex]
[tex]5.75x \geq 35[/tex]
[tex]x \geq \frac{35}{5.75}[/tex]
[tex]x \geq 6.09[/tex]
Since we cannot sell a decimal part of a shirt, at least 7 shirts would need to be sold to cover their costs
