Question

the revenue, in dollars, of a company that produces video game systems can be modeled by the expression $5x^2 + 2x - 80$. the cost, in dollars, of producing the video game systems can be modeled by $5x^2 - x + 100$, where $x$ is the number of video game systems sold. if profit is the difference between the revenue and the cost, what expression represents the profit?

profit can be modeled by the polynomial expression $\boxed{ }$.
if 1,000 video game systems are sold, the companys profit is $$ \boxed{ }$.

Explanation:

Step1: Define profit formula

Profit = Revenue - Cost

Step2: Substitute given expressions

$\text{Profit} = (5x^2 + 2x - 80) - (5x^2 - x + 100)$

Step3: Distribute the negative sign

$\text{Profit} = 5x^2 + 2x - 80 - 5x^2 + x - 100$

Step4: Combine like terms

$\text{Profit} = (5x^2 - 5x^2) + (2x + x) + (-80 - 100) = 3x - 180$

Step5: Substitute $x=1000$ into profit expression

$\text{Profit} = 3(1000) - 180$

Step6: Calculate the numerical value

$\text{Profit} = 3000 - 180 = 2820$

Answer:

Profit can be modeled by the polynomial expression $3x - 180$.
If 1,000 video game systems are sold, the company's profit is $\$2820$.