Julian, an experienced motorcycle mechanic, recently decided to share his expertise by writing and selling an ebook. After conducting some market research, Julian knows that if he charges x dollars per download, he will sell –4x+160 downloads of his ebook in his first year.The online bookstore will charge Julian 25% of the amount he charges per download. So, Julian will earn 75% of the amount he charges per download, or 0.75x dollars, in profit.What two prices can Julian charge per download to earn exactly $900 in profit in his first year?

To find the two prices Julian can charge per download to earn exactly $900 in profit in his first year, we need to set up an equation and solve for x.

The equation is based on the fact that the profit Julian makes is equal to the price he charges per download (0.75x) times the number of downloads he sells (-4x + 160). This profit should be equal to $900.

So, the equation is:

0.75x * (-4x + 160) = 900

Solving this equation for x will give us the two prices Julian can charge per download.

First, distribute 0.75x through the parentheses:

-3x^2 + 120x = 900

Then, subtract 900 from both sides to set the equation equal to zero:

-3x^2 + 120x - 900 = 0

Next, divide every term by -3 to simplify the equation:

x^2 - 40x + 300 = 0

This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. The quadratic formula is the most straightforward method:

x = [40 ± sqrt((40)^2 - 41300)] / (2*1) x = [40 ± sqrt(1600 - 1200)] / 2 x = [40 ± sqrt(400)] / 2 x = [40 ± 20] / 2 x = 20 or x = 60

So, Julian can charge either $20 or$60 per download to earn exactly $900 in profit in his first year.