Question

The marketing department for a video game company determines that the weekly demand for a new video game console can be modeled by the formula , where n is the number of consoles sold each week at price p. Write the equation for n, and then determine approximately how many consoles will sell at a price of $250.

Answer 1

Answer:

Formula for n:

$n=\frac{(300-p)^{2}-1 }{0.04}$

Number sold:

62,475

Step-by-step explanation:

Solving for n:

$p-300=-\sqrt{0.04n+1} \\-p+300=\sqrt{0.04n+1} \\\\(-p+300)^{2} =0.04n+1\\\\(300-p)^{2}-1=0.04n\\\frac{(300-p)^{2}-1}{0.04}=n$

Solving for number sold:

Then replace p with 250, and solve.

Answer 2

The equation for n is n = ((300-p)²-1) / 0.04, The number of consoles sold is 62475.

What is an Equation?

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The weekly demand for a new video game console is given by the equation,

p = 300 - √ ( 0.04n +1)

In the equation , p represents the price of the consoles sold and,

n is the number of consoles sold.

To represent the equation for n, some basic mathematical operations have to be done.

p = 300  - √ ( 0.04n +1)

√ ( 0.04n +1)  = 300 - p

Squaring both the sides of the equation.

0.04n +1 = (300-p)²

0.04n = (300-p)² -1

n = ((300-p)²-1) / 0.04

The consoles sold at a price of $250 has to be determined.

Substituting the value of p in the equation as $250

n = (( 300 - 250)² - 1) / 0.04

n = (50² -1) / 0.04

n = (2500 -1 ) / 0.04

n = 2499 / 0.04

n = 62475

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