the revenue, in dollars, of a company that pr...
the revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x² + 2x - 80. the cost, in dollars, of producing the video game systems can be modeled by 5x² - 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. if 1,000 video game systems are sold, the companys profit is $
Answer
# Explanation:
## Step1: Define profit formula
Profit = Revenue - Cost
## Step2: Substitute given expressions
Revenue = $5x^{2}+2x - 80$, Cost = $5x^{2}-x + 100$. So, Profit=$ (5x^{2}+2x - 80)-(5x^{2}-x + 100)$
## Step3: Simplify the expression
\[
\begin{align*}
&(5x^{2}+2x - 80)-(5x^{2}-x + 100)\\
=&5x^{2}+2x - 80 - 5x^{2}+x - 100\\
=&(5x^{2}-5x^{2})+(2x+x)+(- 80 - 100)\\
=&3x-180
\end{align*}
\]
## Step4: Calculate profit for $x = 1000$
Substitute $x = 1000$ into the profit - expression $3x-180$. Profit=$3\times1000-180=3000 - 180 = 2820$
# Answer:
Profit can be modeled by the polynomial expression $3x - 180$.
If 1,000 video - game systems are sold, the company's profit is $\$2820$.