the demand for a new video game is given by the function p(x)= -x^2 + 5x +75. Correspondingly, the supply function for the same game is given by p(x) = 7x-9, where p represents the price per video in dollars and x represents the number of video games sold in thousands of games. Determine the equilibrium price (where demand equal supply) and the number of video games sold to achieve equilibrium. Solve graphically and algebraically. Use a scale where each box represents 10 units on the y-axis, 1 unit on the x-axis.

Question

the demand for a new video game is given by the function p(x)= -x^2 + 5x +75. Correspondingly, the supply function for the same game is given by p(x) = 7x-9, where p represents the price per video in dollars and x represents the number of video games sold in thousands of games. Determine the equilibrium price (where demand equal supply) and the number of video games sold to achieve equilibrium. Solve graphically and algebraically. Use a scale where each box represents 10 units on the y-axis, 1 unit on the x-axis.

Answer 1

7x-9 = -x^2+5x+75

x^2 + 2 x - 84 = 0

x = [-2 +/- sqrt(4+336) ] /2
= -1 +/- 9.22
= 8.22

Answer 2

I'm guessing you go to John Jay...

Answer 3

To find the equilibrium price and number of video games sold, we need to set the demand equal to the supply and solve for x.

First, let's set the demand and supply functions equal to each other:
- x^2 + 5x + 75 = 7x - 9

Rearranging the equation, we get:
x^2 + 5x - 7x + 75 + 9 = 0
x^2 - 2x + 84 = 0

Now, we can solve this quadratic equation using either the quadratic formula or factoring. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = 84:

x = (-(-2) ± √((-2)^2 - 4(1)(84))) / (2(1))
x = (2 ± √(4 - 336)) / 2
x = (2 ± √(-332)) / 2

Since the term inside the square root is negative, the equation has no real solutions. This means there is no equilibrium point where the demand equals the supply, at least in the given context.