Question

Sadie wants to sell her fan-fiction on the online platform Fanalot. Instead of selling a subscription plan to all of the stories she has written, she decides to sell readers access to each story individually. Her online research suggests that if she charges x dollars per story, she will sell – 5x+100 stories per month. Fanalot will charge Sadie 20% of the amount she charges per story. So, Sadie will earn 80% of the amount she charges per story, or 0.8x dollars, in profit. Which equation can Sadie use to estimate the price she can charge per story to earn $300 in profit each month?

Answer 1

The equation Sadie can use to estimate the price she can charge per story to earn $300 in profit each month is:

0.8x(5x+100) - 0.2x(5x+100) = 300

Simplifying this equation, we get:

4x^2 + 80x - 300 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-80 ± sqrt(80^2 - 4(4)(-300))) / 8

x = (-80 ± sqrt(73600)) / 8

x = (-80 ± 271.23) / 8

x = -43.9 or 7.9

Sadie cannot charge a negative price, so the only possible solution is:

x = 7.9

Therefore, Sadie can charge $7.90 per story to earn $300 in profit each month.