At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that performance, how much below the goal of $2,050 did t... At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that performance, how much below the goal of $2,050 did ticket sales fall?
Understand the Problem
The problem describes a scenario where a cultural center is selling tickets to a play, with adult tickets costing $6.50 and student tickets costing $3.50. The goal is to determine how much the ticket sales fell below the target of $2,050, given that at one performance, the number of student tickets sold was three times the number of adult tickets, and a total of 480 tickets were sold.
Answer
$10
Answer for screen readers
The ticket sales fell below the goal of $2,050 by $10.
Steps to Solve
- Define the variables
Let $d$ be the number of adult tickets sold and $s$ be the number of student tickets sold.
- Write the equations based on the given information
We know that the number of student tickets is three times the number of adult tickets: $s = 3d$. We also know that the total number of tickets sold is 480: $d + s = 480$.
- Solve the system of equations
Substitute $s = 3d$ into the second equation: $d + 3d = 480$ $4d = 480$ $d = \frac{480}{4} = 120$
Now find $s$: $s = 3d = 3(120) = 360$
- Calculate the total revenue from ticket sales
The revenue from adult tickets is $6.50d = 6.50(120) = 780$. The revenue from student tickets is $3.50s = 3.50(360) = 1260$. The total revenue is $780 + 1260 = 2040$.
- Calculate how much the ticket sales fell below the goal
The goal was $2050$, and the actual revenue was $2040$. The difference is $2050 - 2040 = 10$.
The ticket sales fell below the goal of $2,050 by $10.
More Information
The cultural center was very close to meeting their goal, falling only $10 short.
Tips
A common mistake is to misinterpret the relationship between the number of adult and student tickets, or to make an error in solving the system of equations. Another mistake could be in calculating the revenue from the ticket sales. Double-checking each step can help avoid these errors.
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