Question

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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Answer 1

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.