Question

To qualify for gold status of American Airlines one must fly at least 18000 and less than 34200 miles each year if Gerald takes a 900 mile round-trip to visit his parents how many times does Gerald need to visit his parents each year to obtain gold status. explain your answer in interval notation

Answer 1

Let x be the number of times Gerald needs to visit his parents each year; then, the inequality that models the question is

$18000\leq900x\leq34200$

Solving for x,

$\begin{gathered} \Rightarrow\frac{18000}{900}\leq x\leq\frac{34200}{900} \\ \Rightarrow20\leq x\leq38 \\ \Rightarrow x\in\lbrack20,38\rbrack \end{gathered}$

The answer in interval notation is [20,38]