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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=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
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=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

1 answer

To create the linear equations representing the costs at both venues, we need to account for both the fixed rental fee and the variable meal cost per student.

  1. For the Regal Hotel:

    • Fixed cost (rental fee) = $500
    • Variable cost (meal cost per student) = $75 per student
    • Therefore, the equation is: \[ C = 500 + 75s \]

  2. For the Greenhill Country Club:

    • Fixed cost (rental fee) = $1,000
    • Variable cost (meal cost per student) = $65 per student
    • Therefore, the equation is: \[ C = 1000 + 65s \]

Thus, the pair of linear equations that represent this real-world problem is:

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

Of the provided responses, the correct option would be the one that closely matches this formulation. None of the options you provided match correctly, but it means the correct equations are:

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

Please check if there are any alternatives to choose from!