Question

a company sells video games that start at 50$ each and sells 250 video games a week at this price. The company charges more for games that take longer to develop, but they find that for every 2$ increase in the price, 5 fewer video games were sold each week. What is the function that represents this problem? A. Quadratic formula B. Completing the square C. Factoring D. Graphing, E. Square Root

Answer 1

The weekly revenue of a company selling video games and changing prices can be represented by the quadratic linear equation y = ($50 + $2x)(250 - 5x), where y is the total revenue and x is the number of $2 price increases.

Therefore, option A is correct.

Step-by-step explanation:

The function that represents a company selling video games for $50 each and observing a reduction in sales by 5 games for every $2 increase in price can be described by a linear equation. Let y represent the total weekly revenue, and x represent the number of $2 price increases above the base price. Initially, the revenue is $50 × 250 when there are no price increases (x=0). For each increase in price by $2, the revenue changes by selling 5 fewer games, thus decreasing the weekly revenue by $2 × 5. Therefore, the equation representing the weekly revenue as a function of x is: y = ($50 + $2x)(250 - 5x). This equation can be simplified and is indeed quadratic, which means it can be graphed or factored when solving for maximum revenue, for example.