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

1 answer

To create a pair of linear equations that represent the costs for the two venues, we can break down the costs as follows:

  1. Regal Hotel:

    • The ballroom rental fee is $500.
    • The cost per student for the meal is $75.

    Therefore, the equation representing the total cost (C) for the Regal Hotel can be expressed as: \[ C = 75s + 500 \]

  2. Greenhill Country Club:

    • The ballroom rental fee is $1,000.
    • The cost per student for the meal is $65.

    Thus, the equation for the total cost (C) for the Greenhill Country Club is: \[ C = 65s + 1000 \]

Combining these two gives:

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

Therefore, the correct response is: Regal Hotel: \( C = 75s + 500 \); Greenhill Country Club: \( C = 65s + 1000 \).