Question

-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.

Answer 1

Exact answer!!

Subtract 243,600 from both sides of the inequality:

-100x2 + 15,750x + 212,500 ≥243,600

-100x2 + 15,750x + 212,500 − 243,600≥0

-100x2 + 15,750x − 31,100 ≥0

Answer 2

The minimum ticket price is $2.

Explanation:

The inequality is given by

- 100x² + 15750x + 212500 ≥ 243600

⇒ - 100x² + 15750x - 31100 ≥ 0

⇒ - 2x² + 315x - 622 ≥ 0

⇒ -2x² + 311x + 4x - 622 ≥ 0

⇒ (2x - 311)(2 - x) ≥ 0

Now, either (2x - 311) ≥ 0 and (2 - x) ≥ 0

⇒ x ≥ 155.5 and x ≤ 2, which is not possible.

Or, (2x - 311) ≤ 0 and (2 - x) ≤ 0

⇒ x ≤ 155.5 and x ≥ 2, which is a valid range of x-value.

Therefore, the minimum ticket price is $2. (Answer)