To rent a building for a school dance, Ava paid 120plus 2.50 for each student who attended. If she paid a total of $325, how many students attended the dance?
The Correct Answer and Explanation is :
To find out how many students attended the dance, we can set up an equation based on the information given. Ava paid a flat fee of $120 for renting the building and an additional $2.50 for each student who attended. The total cost she incurred was $325.
Step 1: Set Up the Equation
Let ( x ) represent the number of students who attended the dance. The total amount Ava paid can be expressed with the following equation:
[
\text{Total Cost} = \text{Flat Fee} + (\text{Cost per Student} \times \text{Number of Students})
]
Plugging in the values from the problem, we have:
[
325 = 120 + 2.50x
]
Step 2: Solve for ( x )
To isolate ( x ), first subtract the flat fee of $120 from both sides of the equation:
[
325 – 120 = 2.50x
]
This simplifies to:
[
205 = 2.50x
]
Next, divide both sides of the equation by $2.50 to solve for ( x ):
[
x = \frac{205}{2.50}
]
Calculating this gives:
[
x = 82
]
Conclusion
Ava had 82 students attend the dance.
Explanation
In this scenario, we started with the total cost of the event, which includes both a fixed rental fee and a variable cost based on attendance. The approach to solving the problem involved breaking down the total payment into its components: the fixed cost and the cost per attendee. By creating an algebraic equation and performing basic arithmetic operations (subtraction and division), we were able to isolate the variable ( x ), which represented the number of students.
This method can be applied to various real-world situations where costs are structured with both fixed and variable components. Understanding how to set up and solve equations is a vital skill, particularly in budgeting and planning events.