Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?
$5n - 300 = 1,500$
$5n + 300 = 1,500$
$5n - 200 + 100n = 1,500$
$5n - 100 - 200n = 1,500
Answer (1)
Calculate total expenses: DJ ($200) + decorations ($100) = $300.
Calculate total revenue: $5 per student, so 5 n .
Calculate profit: Total revenue - total expenses = 5 n − 300 .
Set profit to $1,500: 5 n − 300 = 1500 , which is the required equation. 5 n − 300 = 1 , 500
Explanation
Understanding the Problem Let's break down the problem. We need to find an equation that represents the soccer team's profit from the school dance. The profit is the revenue (money coming in) minus the expenses (money going out).
Calculating Total Expenses First, let's calculate the total expenses. The DJ costs $200 and the decorations cost $100. So the total expenses are: 200 + 100 = 300 The total expenses are $300.
Calculating Total Revenue Next, let's calculate the total revenue. The team charges $5 per student, and 'n' represents the number of students attending. So the total revenue is: 5 × n = 5 n The total revenue is $5n.
Calculating Profit Now, let's calculate the profit. The profit is the total revenue minus the total expenses: P ro f i t = T o t a l R e v e n u e − T o t a l E x p e n ses P ro f i t = 5 n − 300
Setting up the Equation We know the team wants to make $1,500 in profit. So we set the profit equal to $1,500: 5 n − 300 = 1500 This is the equation we need to find the number of students needed to make $1,500 in profit.
Final Answer Therefore, the correct equation is: 5 n − 300 = 1500
Examples
Imagine you're organizing a bake sale to raise money for a school trip. You have fixed costs like ingredients (say, $50) and you plan to sell each cookie for $2. If you want to make a profit of $200, you can use a similar equation to figure out how many cookies you need to sell. If 'c' is the number of cookies, the equation would be 2 c − 50 = 200 . This kind of problem helps you plan and manage finances effectively in everyday situations.
