We created this inequality to represent how Amy can meet her revenue goals: -100x2 + 15,750x + 212,500 ≥ 243,600

In this activity, you’ll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.

Part A

Set the inequality greater than or equal to 0.

Part B

Simplify the inequality by dividing by the GCF so the leading coefficient is positive.

Part C

Factor the left side of the inequality by grouping.

Part D

Solve the quadratic inequality. Remember to check any possible solutions for viability.

Part E

What is the minimum number of $2 increases that Amy needs to apply to the ticket price to reach her desired revenue?

Part F

What’s the minimum ticket price that Amy can charge and reach her goal? Recall that the ticket price is represented by 25 + 2x, where x represents the number of $2 increases.