Let’s break down the problem step by step:
1. Identify the costs involved:
- The DJ's charge is \[tex]$200.
- The cost of decorations is \$[/tex]100.
- Therefore, the total cost of the dance is:
[tex]\[
200 + 100 = \$300
\][/tex]
2. Determine the profit goal:
- The team wants to make a profit of \[tex]$1,500.
3. Charge per student:
- Each student is charged \$[/tex]5.00 to attend the dance.
4. Let [tex]\( n \)[/tex] represent the number of students attending the dance.
5. Formulate the equation:
- The income from [tex]\( n \)[/tex] students is [tex]\( 5n \)[/tex] dollars.
- To achieve the desired profit, the income minus the total costs should equal the required profit:
[tex]\[
5n - 300 = 1500
\][/tex]
6. Check the given options:
- The correct equation fits:
[tex]\[
5n - 300 = 1500
\][/tex]
This equation accurately represents the situation where:
- [tex]\( 5n \)[/tex] is the total income from students.
- Subtracting the total cost of \[tex]$300 from this income.
- The result is the desired profit of \$[/tex]1,500.
Thus, the correct equation to find the number of students needed to make \$1,500 in profit is:
[tex]\[
5n - 300 = 1500
\][/tex]
