The revenue, in dollars, of a company that produces video game systems can be modeled by the expression [tex]$5 x^2+2 x-80$[/tex]. The cost, in dollars, of producing the video game systems can be modeled by [tex]$5 x^2-x+100$[/tex], where [tex]$x$[/tex] 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 company [ ]

A. x+20
B. x-180
C. 3x+20
D. 3x-180

The expression representing the profit is 3 x − 180 . If 1,000 video game systems are sold, the company will make a profit of $2,820. Thus, the correct answer is option D, 3 x − 180 .
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Answered by Anonymous | 2025-07-04

Define Profit as Revenue - Cost.
Substitute the given expressions: Profit = ( 5 x 2 + 2 x − 80 ) − ( 5 x 2 − x + 100 ) .
Simplify the expression: Profit = 3 x − 180 .
Evaluate the profit for x = 1000 : Profit = $2820 .

Explanation

Understanding the Problem Let's break down this problem step by step. We're given expressions for revenue and cost, and we need to find an expression for profit. Profit is simply the difference between revenue and cost. Then, we'll evaluate the profit when 1,000 video game systems are sold.

Defining the Variables We know that:


Revenue = 5 x 2 + 2 x − 80
Cost = 5 x 2 − x + 100
Profit = Revenue - Cost

Calculating the Profit Expression Now, let's find the expression for profit by subtracting the cost from the revenue:

Profit = ( 5 x 2 + 2 x − 80 ) − ( 5 x 2 − x + 100 )
Profit = 5 x 2 + 2 x − 80 − 5 x 2 + x − 100
Profit = ( 5 x 2 − 5 x 2 ) + ( 2 x + x ) + ( − 80 − 100 )
Profit = 0 + 3 x − 180
Profit = 3 x − 180

Calculating Profit for 1000 Systems So, the expression that represents the profit is 3 x − 180 . Now, we need to find the profit when 1,000 video game systems are sold. We substitute x = 1000 into the profit expression:

Profit = 3 ( 1000 ) − 180
Profit = 3000 − 180
Profit = 2820

Final Answer Therefore, the profit when 1,000 video game systems are sold is $2820 .

Examples
Understanding profit calculation is crucial in business. For example, if you're selling lemonade, knowing your revenue (money from sales) and costs (lemons, sugar, cups) helps you calculate your profit. If you sell 100 cups of lemonade for $1 each (revenue = $100) and your costs are $20, your profit is $100 - $20 = $80. This simple calculation helps you decide if your lemonade stand is worth the effort and how you might increase your earnings.

Answered by GinnyAnswer | 2025-07-04