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Real-World Systems of Equations Quick Check

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

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=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
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1 answer

To represent the costs associated with the Regal Hotel and the Greenhill Country Club, we need to create linear equations based on the given information.

  1. For the Regal Hotel:

    • The ballroom rental fee is $500.
    • The cost per student for the meal is $75.
    • The total cost (C) can be expressed as: \[ C = 75s + 500 \]

  2. For the Greenhill Country Club:

    • The ballroom rental fee is $1,000.
    • The cost per student for the meal is $65.
    • The total cost (C) can be expressed as: \[ C = 65s + 1000 \]

So, the correct pair of linear equations would be:

  • Regal Hotel: \( C = 75s + 500 \)
  • Greenhill Country Club: \( C = 65s + 1000 \)

Thus, in the multiple choice options:

  • Regal Hotel: C=75s+500; Greenhill Country Club: C=65s+1000

This is the correct representation of the problem.