The revenue R from selling x handheld video games is given by R = x(180 – 1.5x). Find the number of handheld video games that must be sold to produce a revenue of $5400. Show your work

Answer 1

We are given the expected revenue (R), which means we just need to solve for X.

The original equation is R = x(180 - 1.5x). Let's go ahead and put $5400 in for R.

5400 = x(180 - 1.5x). Next, let's multiply the values in parenthesis by x. We then get:

5400 = 180x - 1.5x^2. Next, subtract 180x and -1.5x^2 from the right side of the equation:

1.5x^2 - 180x + 5400 = 0.

We want to work with integers, so let's bring that 1.5x^2 up to a whole number. We can do this by multiplying the entire equation by 2:

2 (1.5x^2 - 180x + 5400) = 3x^2 -360x + 10800

This makes things a little easier! We can factor from here. We can see three goes into each, so let's divide the equation by 3.

(3x^2 - 360x + 10800) / 3 = x^2 - 120x + 3600.

We can factor further from here: 3 (x-60)(x-60). x = 60!