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

1 answer

To create the linear equations for the prom cost associated with each venue, we need to correctly incorporate the fixed costs (rental fees) and the variable costs (cost per student for meals).

  1. Regal Hotel:

    • Fixed cost (ballroom rental fee): $500
    • Variable cost (meal per student): $75 per student
    • Total cost equation: \[ C = 500 + 75s \]

  2. Greenhill Country Club:

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

Now let's express these equations correctly:

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

So, the correct pair of linear equations representing this real-world problem is:

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

Among the response options, you would look for something that resembles these equations correctly.