To qualify for Gold status at Awesome Airlines, one must fly at least 11000
 and less than 22000
 miles each year.  If Elliot takes a 550
-mile round-trip flight to visit his parents, how many times does Elliot need to visit his parents each year to attain Gold status?  Express your answer in interval notation.  

To solve this problem, we need to determine how many round-trip flights Elliot must take in a year to fly between 11,000 and 22,000 miles, thus qualifying for Gold status at Awesome Airlines.

### Step 1: Set up the equation
Each round-trip flight to visit his parents covers 550 miles. If Elliot takes \( x \) round-trip flights, the total miles flown is given by:

\[
\text{Total miles} = 550x
\]

We are asked to find the values of \( x \) that make this total lie within the interval from 11,000 to 22,000 miles. Therefore, we need to solve the following inequality:

\[
11000 \leq 550x < 22000
\]

### Step 2: Solve the inequality
#### Solve the left side:
\[
11000 \leq 550x
\]
Divide both sides by 550:
\[
\frac{11000}{550} \leq x
\]
\[
x \geq 20
\]

#### Solve the right side:
\[
550x < 22000
\]
Divide both sides by 550:
\[
x < \frac{22000}{550}
\]
\[
x < 40
\]

### Step 3: Combine the results
From both parts of the inequality, we find that:
\[
20 \leq x < 40
\]

### Step 4: Express the solution in interval notation
The number of times Elliot must visit his parents each year to attain Gold status is:
\[
[20, 40)
\]

This means Elliot needs to take at least 20 but fewer than 40 round-trip flights per year to qualify for Gold status.

---

Would you like further details or have any other questions? 

Here are 5 related questions:
1. How would the solution change if each round-trip flight were 600 miles instead of 550?
2. What if Elliot needs to fly at least 12,000 miles? What would the interval become?
3. How many miles will Elliot fly if he takes exactly 25 round trips?
4. How many additional miles does Elliot need to reach Gold status after 15 round-trip flights?
5. What if the maximum miles for Gold status were raised to 25,000 miles?

**Tip**: For inequalities, always check if endpoints are included (closed or open intervals) based on the given conditions!

To qualify for Gold status at Awesome Airlines, one must fly at least 11000 and less than 22000 miles each year. If Elliot takes a 550-mile round-trip flight to visit his parents, how many times does Elliot need to visit his parents each year to attain Gold status? Express your answer in interval notation.

Solve a real-world problem involving inequalities and linear equations. Learn how many 550-mile round trips are needed to fly between 11,000 and 22,000 miles to attain Gold status at Awesome Airlines. Suitable for students in Grades 7-9.

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