A teacher can spend as much as $125.00 to take students to a movie. ​ ​A movie theater charges a $10.00 group fee and $5.50 per ticket. ​ ​Which of the following inequalities represents the problem and could ​be solved to find the maximum number of students, X , who could ​attend the movie?

The problem involves determining the maximum number of students, $ X $, that a teacher can take to a movie given a $125 budget, where the movie theater charges a $10 group fee and $5.50 per ticket.

The inequality representing the problem can be set up by considering the total cost, which includes the group fee and the cost of $ X $ tickets. The total cost must not exceed the budget of $125.

### Step-by-step breakdown:
1. **Group fee**: $10.00 (constant).
2. **Cost per student**: $5.50.
3. **Total cost for $ X $ students**: $ 5.50X $.
4. **Total cost equation**: Add the group fee and the cost for $ X $ students:
   \[
   10 + 5.50X
   \]
5. **Inequality**: This total cost should not exceed $125, so:
   \[
   10 + 5.50X \leq 125
   \]

Now, let's solve for $ X $ (the number of students):

\[
10 + 5.50X \leq 125
\]

Subtract 10 from both sides:

\[
5.50X \leq 115
\]

Now, divide both sides by 5.50:

\[
X \leq \frac{115}{5.50} = 20.91
\]

Since $ X $ represents the number of students, it must be a whole number. So the maximum number of students is **20**.

### Inequality:
The inequality that represents the situation is:

\[
10 + 5.50X \leq 125
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the inequality look like if the group fee were $15 instead of $10?
2. How would the solution change if each ticket cost $6.00 instead of $5.50?
3. How would the problem change if the budget was increased to $150?
4. What is the effect of increasing the number of students by 5 on the total cost?
5. How would the maximum number of students change if the group fee were waived?

**Tip**: Always double-check the setup of your inequality before solving, as misinterpreting the components can lead to incorrect results.

A teacher can spend as much as $125.00 to take students to a movie. A movie theater charges a $10.00 group fee and $5.50 per ticket. Which of the following inequalities represents the problem and could be solved to find the maximum number of students, X, who could attend the movie?

Learn how to solve a budget-related word problem using inequalities. A teacher can spend up to $125 on a movie trip with a $10 group fee and $5.50 per student. Find out how to calculate the maximum number of students that can attend using a linear inequality.

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