### Instruction: The amount of money a certain company has can be modeled with the line $y=-265x+2800$, where $x$ is the number of workers the company decides to hire. What is the maximum number of workers the company can hire before the company has no money left and goes bankrupt?### Response: To answer this question, I need to find the value of $x$ that makes $y=0$, since that means the company has no money left.
I can do this by setting $y=0$ and solving for $x$.
So I have $0=-265x+2800$.
To isolate $x$, I can add $265x$ to both sides, which gives me $265x=2800$.
Then I can divide both sides by $265$, which gives me $x=2800/265$.
I can simplify this fraction by dividing the numerator and denominator by $5$, which gives me $x=560/53$.
This is a fraction, but it doesn't make sense to hire a fraction of a worker, so I need to round this down to the nearest integer, since rounding up would mean hiring more workers than I can afford.
The nearest integer that is less than or equal to $560/53$ is $10$, so the maximum number of workers the company can hire is $10$.