- Identify the relationship between the total number of tickets, student tickets \(c\), and adult tickets \(a\): \(c + a = 67\).
- Solve the equation for \(c\) by isolating it: \(c = 67 - a\).
- Match the result with the given options to confirm the expression is \(67 - a\).
- The final answer is \(\boxed{67 - a}\).
Explanation
- Analyzing the Given Data
To determine the number of student tickets sold, let's analyze the information provided about the school production. We are given the total number of tickets purchased and the cost for each type of ticket. Let \(c\) represent the number of student tickets and \(a\) represent the number of adult tickets. The problem states that the total number of tickets purchased is 67. We can represent this relationship with the following equation:
\[c + a = 67\]
- Solving for the Number of Student Tickets
We need to express \(c\) in terms of \(a\) to identify the correct entry for the 'Tickets Sold' column for students in the table. Starting from the equation established in the previous step, \(c + a = 67\), we can isolate \(c\) by subtracting \(a\) from both sides of the equation:
\[c = 67 - a\]
This expression represents the number of student tickets sold based on the total number of tickets and the number of adult tickets. Comparing this result with the given options, we can see that \(67 - a\) is the correct expression.
- Final Conclusion
The expression for the number of student tickets sold is \(\boxed{67 - a}\).
Examples
This algebraic approach is frequently used in resource management and budgeting. For instance, if a store sells two types of items and you know the total quantity sold but only have the count for one type, you can easily calculate the other. This method ensures that inventory or budget constraints are consistently met, helping in making informed decisions about sales strategies or resource allocation.