Real-World Systems of Equations Quick Check

Question

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Question
The senior class at Hartford High School is planning their prom. They’ve narrowed the location down to two choices. The Regal Hotel charges, C, $500 for the ballroom rental fee and $75 per student, s, for the meal. The Greenhill Country Club charges, C, $1,000 for the ballroom rental fee and $65 per student, s, for the meal. Create a pair of linear equations that represent this real-world problem.(1 point)
Responses

Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000
Regal Hotel: upper C equals 75 s plus 500 ; Greenhill Country Club: upper C equals 65 s plus 1,000

Regal Hotel: C=75s+1,000; Greenhill Country Club: C=65s+500
Regal Hotel: upper C equals 75 s plus 1,000 ; Greenhill Country Club: upper C equals 65 s plus 500

Regal Hotel: C=500s+75; Greenhill Country Club: C=1,000s+65
Regal Hotel: upper C equals 500 s plus 75 ; Greenhill Country Club: upper C equals 1,000 s plus 65

Regal Hotel: C=1,000s+75; Greenhill Country Club: C=500s+65

Answer 1

To create a pair of linear equations for the costs of the two locations for the prom, we need to correctly represent the rental fee and the cost per student.

1. Regal Hotel: The total cost (C) is given by a fixed rental fee of $500 plus $75 for each student (s). This can be expressed as: \[ C = 75s + 500 \]

2. Greenhill Country Club: The total cost (C) is a fixed rental fee of $1,000 plus $65 for each student (s). This can be expressed as: \[ C = 65s + 1,000 \]

So, the correct pair of linear equations is:

• Regal Hotel: \( C = 75s + 500 \)
• Greenhill Country Club: \( C = 65s + 1,000 \)

The correct response to your question is: Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1,000.