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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.

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To create a pair of linear equations representing the total cost of the prom at each location, we need to express the total cost, \( C \), as a function of the number of students, \( s \).

For the Regal Hotel:

The total cost at Regal Hotel can be represented by the equation: \[ C = 500 + 75s \] Where:

  • \( 500 \) is the fixed ballroom rental fee.
  • \( 75s \) is the cost of the meal per student.

For the Greenhill Country Club:

The total cost at Greenhill Country Club can be represented by the equation: \[ C = 1000 + 65s \] Where:

  • \( 1000 \) is the fixed ballroom rental fee.
  • \( 65s \) is the cost of the meal per student.

Summary of the equations:

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

These equations can be used to compare the total costs at both venues based on the number of students attending.