Question

A business offers educational tours to Patagonia, a region of South America that includes parts of Chile and Argentina. The profit P for x number of persons is P(x) = −25x^2 + 1250x − 5000. The trip will be rescheduled if the profit is less than $7500. How many people must have signed up if the trip is rescheduled?

Answer 1

13.82 or 14 people

Explanation:

Step 1: Set equation equal to 7500

7500 = -25x² + 1250x - 5000

Step 2: Solve

0 = -25x² + 1250x - 12500

0 = -25(x² - 50x + 500)

0 = x² - 50x + 500

When you use the quadratic formula, you should get 13.82, rounded to 14 people as your answer.

Alternatively, we can graph the expression and see where $7500 for x people is.