Tickets to a baseball game cost $3 for a child's ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace $x$ in the table so that a single variable equation can be written and solved to determine the number of child's tickets, $c$, sold?
| | Tickets sold | Cost | Total |
| :----- | :----------- | :--- | :---- |
| Child | c | 3 | $3c$ |
| Adult | $x$ | 5 | $5x$ |
| Total | | | |
A. 139
B. 521
C. 139 - c
D. 521 - c
Answer (1)
Express the total number of people attended in terms of c and x: c + x = 139 .
Express the total amount collected in terms of c and x: 3 c + 5 x = 521 .
Solve the first equation for x in terms of c: x = 139 − c .
The value that could replace x is 139 − c , so the final answer is 139 − c .
Explanation
Problem Analysis Let's analyze the given information to determine which value could replace x in the table to create a single-variable equation in terms of c .
Known Information We know the following:
Cost of a child's ticket: $3
Cost of an adult's ticket: $5
Total amount collected: $521
Total number of people attended: 139
c = number of child tickets
x = number of adult tickets
Setting up Equations We can set up two equations based on the given information:
The total number of people: c + x = 139
The total amount collected: 3 c + 5 x = 521
Expressing x in terms of c Our goal is to express x in terms of c so that we can substitute it into the second equation and obtain a single-variable equation in terms of c . From the first equation, we can isolate x :
x = 139 − c
Substitution Now, we can substitute this expression for x into the second equation:
3 c + 5 ( 139 − c ) = 521
Conclusion The value that could replace x in the table so that a single-variable equation can be written and solved to determine the number of child's tickets, c , sold is 139 − c .
Examples
Understanding how to create single-variable equations is useful in many real-world scenarios. For example, if you're planning a school event and have a budget, you can use this method to determine how many tickets you can sell at different prices to meet your financial goals. Similarly, businesses use this approach to optimize pricing strategies and manage inventory based on sales data.
