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 equation $250 = 300 - \sqrt{0.04n + 1}$, where $n$ is the number of consoles sold each week at a price of $250. what is the value of $n$? select the correct answer. $\bigcirc$ $n = 62,525$ $\bigcirc$ $n = 62,475$ $\bigcirc$ $n = 6,225$ $\bigcirc$ $n = 2,525$

Explanation:

Step1: Isolate the square root term

Subtract 300 from both sides, then multiply by -1.
$250 - 300 = -\sqrt{0.04n + 1}$
$-50 = -\sqrt{0.04n + 1}$
$\sqrt{0.04n + 1} = 50$

Step2: Eliminate the square root

Square both sides of the equation.
$(\sqrt{0.04n + 1})^2 = 50^2$
$0.04n + 1 = 2500$

Step3: Solve for the linear term

Subtract 1 from both sides.
$0.04n = 2500 - 1$
$0.04n = 2499$

Step4: Calculate the value of n

Divide both sides by 0.04.
$n = \frac{2499}{0.04}$
$n = 62475$

Answer:

n = 62,475