To find the equation that can be used to determine the number of students needed to attend the dance to make a \[tex]$1,500 profit, let's break down the costs and income step-by-step.
### Step-by-Step Solution:
1. Calculate Fixed Costs:
The total fixed costs for organizing the dance include:
- DJ charges: \$[/tex]200
- Decorations cost: \[tex]$100
Total fixed costs = \$[/tex]200 + \[tex]$100 = \$[/tex]300
2. Determine Profit Requirement:
The team wants to make a profit of \[tex]$1,500 from the dance.
3. Determine Income from Tickets:
Each student is charged \$[/tex]5.00 for a ticket. Thus, if [tex]\( n \)[/tex] represents the number of students attending the dance, the income from ticket sales is:
[tex]\[
\text{Income} = 5n
\][/tex]
where [tex]\( n \)[/tex] is the number of students.
4. Formulate the Profit Equation:
To find out how many students are needed to make a \$1,500 profit, we need to set up the equation considering both the income and the costs. The profit equation can be formulated as:
[tex]\[
\text{Profit} = \text{Income from tickets} - \text{Fixed costs}
\][/tex]
In mathematical terms:
[tex]\[
1{,}500 = 5n - 300
\][/tex]
So, the correct equation that represents the situation is:
[tex]\[
5n - 300 = 1{,}500
\][/tex]
None of the other options such as [tex]\( 5n + 300 = 1{,}500 \)[/tex], [tex]\( 5n - 200 + 100n = 1{,}500 \)[/tex], or [tex]\( 5n - 100 - 200n = 1{,}500 \)[/tex] correctly model the income and cost relationship as described.
Therefore, the correct answer is:
[tex]\[
5n - 300 = 1,500
\][/tex]
