Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than $14 on x student tickets and 1 adult ticket, what is one possible value of x ?

Answer

To solve the problem step by step, we will set up an inequality based on the information given about ticket prices and the total amount spent.

### Step 1: Define the Variables
Let:
- \( x \) = number of student tickets
- Cost of student ticket = $2
- Cost of adult ticket = $3
- Number of adult tickets = 1

### Step 2: Write the Total Cost Equation
The total cost for the tickets can be expressed as:
\[ \text{Total Cost} = \text{Cost of Adult Ticket} + \text{Cost of Student Tickets} \]
This can be written as:
\[ \text{Total Cost} = 3 + 2x \]

### Step 3: Set Up the Inequality
According to the problem, Chris spends at least $11 but no more than $14. Therefore, we can write the inequality as:
\[ 11 \leq 3 + 2x \leq 14 \]

### Step 4: Break Down the Inequality
We can break this compound inequality into two separate inequalities:
1. \( 3 + 2x \geq 11 \)
2. \( 3 + 2x \leq 14 \)

### Step 5: Solve the First Inequality
Starting with the first inequality:
\[ 3 + 2x \geq 11 \]
Subtract 3 from both sides:
\[ 2x \geq 8 \]
Now, divide by 2:
\[ x \geq 4 \]

### Step 6: Solve the Second Inequality
Now, solve the second inequality:
\[ 3 + 2x \leq 14 \]
Subtract 3 from both sides:
\[ 2x \leq 11 \]
Now, divide by 2:
\[ x \leq 5.5 \]

### Step 7: Combine the Results
From the two inequalities, we have:
\[ 4 \leq x \leq 5.5 \]

### Step 8: Determine Possible Values of \( x \)
Since \( x \) represents the number of student tickets, it must be a whole number. The possible integer values for \( x \) in the range \( 4 \leq x \leq 5.5 \) are:
- \( x = 4 \)
- \( x = 5 \)

### Conclusion
One possible value of \( x \) is \( 5 \).