Question

To qualify for gold status at American Airlines one must fly less than 27500 but at least 9900 miles each year if Gerald takes a 550 mile round-trip flight when visiting his parents how many times does Gerald need to visit his parents each year to attain gold status. Express your answer in interval notation

Answer 1

Answer: [18, 50)

Step-by-step explanation:

Let x represent the number of times that Gerald needs to visit his parents each year to attain gold status. A visit is a round trip of 550 miles. Thus, the number of miles for x visits is

550 * x = 550x

In a year, the distance travelled must be at least 9900 miles. This means that

550x ≥ 9900

By reversing the inequality, It can also be written as

9900 ≤ 550x

To attain a gold status, the distance travelled must be less than 27500. This means that

550x < 27500

By combining the inequalities, we have

9900 ≤ 550x < 27500

Dividing through by 550, it becomes

9900/550 ≤ 550x/550 < 27500/550

18 ≤ x < 50

In interval notation, it becomes

[18, 50)