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Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges [tex]$\$[/tex] 200[tex]$ and decorations cost $[/tex]\[tex]$ 100$[/tex]. The team decides to charge each student [tex]$\$[/tex] 5.00[tex]$ to attend the dance. If $[/tex]n[tex]$ represents the number of students attending the dance, which equation can be used to find the number of students needed to make $[/tex]\[tex]$ 1,500$[/tex] in profit?

A. [tex]$5n - 300 = 1,500$[/tex]
B. [tex]$5n + 300 = 1,500$[/tex]
C. [tex]$5n - 200 + 100n = 1,500$[/tex]
D. [tex]$5n - 100 - 200n = 1,500$[/tex]



Answer :

GinnyAnswer
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]

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